Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T01:48:01.043Z Has data issue: false hasContentIssue false

Bibliography

Published online by Cambridge University Press:  11 May 2017

Vladas Pipiras
Affiliation:
University of North Carolina, Chapel Hill
Murad S. Taqqu
Affiliation:
Boston University
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] J., Aaronson and M., Denker. Characteristic functions of random variables attracted to 1-stable laws. The Annals of Probability, 26(1):399–415, 1998. (Cited on pages 583 and 586.)Google Scholar
[2] K. M., Abadir, W., Distaso and L., Giraitis. Nonstationarity-extended local Whittle estimation. Journal of Econometrics, 141(2):1353–1384, 2007. (Cited on page 572.)Google Scholar
[3] K. M., Abadir, W., Distaso and L., Giraitis. Two estimators of the long-run variance: beyond short memory. Journal of Econometrics, 150(1):56–70, 2009. (Cited on page 28.)Google Scholar
[4] J., Abate and W., Whitt. The Fourier-series method for inverting transforms of probability distributions. Queueing Systems. Theory and Applications, 10(1-2):5–87, 1992. (Cited on page 271.)Google Scholar
[5] P., Abry and G., Didier. Wavelet estimation of operator fractional Brownian motions. To appear in Bernoulli. Preprint, 2015. (Cited on page 536.)
[6] P., Abry and V., Pipiras. Wavelet-based synthesis of the Rosenblatt process. Signal Processing, 86(9):2326–2339, 2006. (Cited on page 465.)Google Scholar
[7] P., Abry and F., Sellan. The wavelet-based synthesis for the fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation. Applied and Computational Harmonic Analysis, 3(4):377–383, 1996. (Cited on page 465.)Google Scholar
[8] P., Abry and D., Veitch. Wavelet analysis of long range dependent traffic. IEEE Transactions on Information Theory, 44(1):2–15, 1998. (Cited on page 111.)Google Scholar
[9] P., Abry, D., Veitch and P., Flandrin. Long-range dependence: revisiting aggregation with wavelets. Journal of Time Series Analysis, 19(3):253–266, 1998. (Cited on page 112.)Google Scholar
[10] P., Abry, P., Flandrin, M. S., Taqqu, and D., Veitch. Self-similarity and long-range dependence through the wavelet lens. In P., Doukhan, G., Oppenheim, and M. S., Taqqu, editors, Theory and Applications of Long-Range Dependence, pages 527–556. Birkhäuser, 2003. (Cited on page 112.)
[11] P., Abry, P., Chainais, L., Coutin and V., Pipiras. Multifractal random walks as fractional Wiener integrals. IEEE Transactions on Information Theory, 55(8):3825–3846, 2009. (Cited on page 612.)Google Scholar
[12] P., Abry, P., Borgnat, F., Ricciato, A., Scherrer and D., Veitch. Revisiting an old friend: on the observability of the relation between long range dependence and heavy tail. Telecommunication Systems, 43(3-4):147–165, 2010. (Cited on page 224.)Google Scholar
[13] S., Achard and I., Gannaz. Multivariate wavelet Whittle estimation in long-range dependence. Journal of Time Series Analysis, 2015. (Cited on page 574.)
[14] S., Achard, D. S., Bassett, A. Meyer-Lindenberg, and E. Bullmore. Fractal connectivity of long-memory networks. Physical Review E, 77:036104, Mar 2008. (Cited on page 537.)
[15] C., Agiakloglou, P., Newbold and M., Wohar. Bias in an estimator of the fractional difference parameter. Journal of Time Series Analysis, 14(3):235–246, 1993. (Cited on pages 111 and 573.)Google Scholar
[16] N. U., Ahmed and C., D. Charalambous. Filtering for linear systems driven by fractional Brownian motion. SIAM Journal on Control and Optimization, 41(1):313–330, 2002. (Cited on page 395.)Google Scholar
[17] H., Akaike. Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory (Tsahkadsor, 1971), pages 267–281. Budapest: Akadémiai Kiadó, 1973. (Cited on page 552.)
[18] J. M. P., Albin. A note on Rosenblatt distributions. Statistics & Probability Letters, 40(1):83–91, 1998. (Cited on page 281.) 613Google Scholar
[19] D. W., Allan. Statistics of atomic frequency standards. Proceedings of the IEEE, 54(2):221– 230, 1966. (Cited on page 112.)Google Scholar
[20] E., Alòs and D., Nualart. Stochastic integration with respect to the fractional Brownian motion. Stochastics and Stochastics Reports, 75(3):129–152, 2003. (Cited on page 412.)Google Scholar
[21] E., Alòs, O., Mazet, and D., Nualart. Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 12. Stochastic Processes and their Applications, 86(1):121–139, 2000. (Cited on page 435.)Google Scholar
[22] E., Alòs, O., Mazet, and D., Nualart. Stochastic calculus with respect to Gaussian processes. The Annals of Probability, 29(2):766–801, 2001. (Cited on page 435.)Google Scholar
[23] F., Altissimo, B., Mojon and P., Zaffaroni. Can aggregation explain the persistence of inflation? Journal of Monetary Economics, 56(2):231–241, 2009. (Cited on page 224.)Google Scholar
[24] E., Alvarez-Lacalle, B., Dorow, J.-P., Eckmann, and E., Moses. Hierarchical structures induce long-range dynamical correlations in written texts. Proceedings of the National Academy of Sciences, 103(21):7956–7961, 2006. (Cited on page 228.)Google Scholar
[25] P.-O., Amblard and J.-F., Coeurjolly. Identification of the multivariate fractional Brownian motion. Signal Processing, IEEE Transactions on, 59(11):5152–5168, nov. 2011. (Cited on pages 488 and 536.)
[26] P.-O., Amblard, J.-F., Coeurjolly, F., Lavancier, and A., Philippe. Basic properties of the multivariate fractional Brownian motion. Séminaires & Congrès, 28:65–87, 2012. (Cited on pages 534 and 536.)Google Scholar
[27] A., Amirdjanova. Nonlinear filtering with fractional Brownian motion. Applied Mathematics and Optimization, 46(2-3):81–88, 2002. Special issue dedicated to the memory of Jacques-Louis Lions. (Cited on page 436.)Google Scholar
[28] A., Amirdjanova and M., Linn. Stochastic evolution equations for nonlinear filtering of random fields in the presence of fractional Brownian sheet observation noise. Computers & Mathematics with Applications. An International Journal, 55(8):1766–1784, 2008. (Cited on page 436.)Google Scholar
[29] T. G., Andersen and T., Bollerslev. Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance, 4(2):115–158, 1997. (Cited on page 611.)Google Scholar
[30] T. G., Andersen, T., Bollerslev, F. X., Diebold, and H., Ebens. The distribution of realized stock return volatility. Journal of Financial Economics, 61(1):43–76, 2001. (Cited on page 611.)Google Scholar
[31] J., Andersson. An improvement of the GPH estimator. Economics Letters, 77(1):137–146, 2002. (Cited on page 111.)Google Scholar
[32] D. W. K., Andrews and P., Guggenberger. A bias-reduced log-periodogram regression estimator for the long-memory parameter. Econometrica, 71(2):675–712, 2003. (Cited on page 111.)Google Scholar
[33] D. W. K., Andrews and O., Lieberman. Valid Edgeworth expansions for the Whittle maximum likelihood estimator for stationary long-memory Gaussian time series. Econometric Theory, 21(4):710–734, 2005. (Cited on page 571.)Google Scholar
[34] D. W. K., Andrews and Y., Sun. Adaptive local polynomial Whittle estimation of long-range dependence. Econometrica, 72(2):569–614, 2004. (Cited on pages 560, 561, 565, 566, and 572.)Google Scholar
[35] G. E., Andrews, R., Askey and R., Roy. Special Functions, volume 71 of Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press, 1999. (Cited on pages 280, 526, and 527.)
[36] V. V., Anh and K. E., Lunney. Parameter estimation of random fields with long-range dependence. Mathematical and Computer Modelling, 21(9):67–77, 1995. (Cited on page 537.)Google Scholar
[37] V. V., Anh, N., Leonenko and A., Olenko. On the rate of convergence to Rosenblatt-type distribution. Journal of Mathematical Analysis and Applications, 425(1):111–132, 2015. (Cited on page 343.)Google Scholar
[38] C. F., Ansley and R., Kohn. A note on reparameterizing a vector autoregressive moving average model to enforce stationarity. Journal of Statistical Computation and Simulation, 24(2):99–106, 1986. (Cited on page 570.)Google Scholar
[39] N., Antunes, V., Pipiras, P., Abry and D., Veitch. Small and large scale behavior of moments of Poisson cluster processes. Preprint, 2016. (Cited on page 224.)
[40] D., Applebaum. Lévy Processes and Stochastic Calculus, 2nd edition volume 116 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2009. (Cited on page 268.)
[41] V. F., Araman and P., W. Glynn. Fractional Brownian motion with H < 12 as a limit of scheduled traffic. Journal of Applied Probability, 49(3):710–718, 2012. (Cited on page 225.)Google Scholar
[42] M. A., Arcones. Limit theorems for non-linear functionals of a stationary Gaussian sequence of vectors. The Annals of Probability, 22:2242–2274, 1994. (Cited on page 344.)Google Scholar
[43] M. A., Arcones. Distributional limit theorems over a stationary Gaussian sequence of random vectors. Stochastic Processes and their Applications, 88(1):135–159, 2000. (Cited on page 344.)Google Scholar
[44] B., Arras. On a class of self-similar processes with stationary increments in higher order Wiener chaoses. Stochastic Processes and their Applications, 124(7):2415–2441, 2014. (Cited on page 281.)Google Scholar
[45] B., Arras. A white noise approach to stochastic integration with respect to the Rosenblatt process. Potential Analysis, 43(4):547–591, 2015. (Cited on page 435.)Google Scholar
[46] R., Arratia. The motion of a tagged particle in the simple symmetric exclusion system on Z. The Annals of Probability, 11(2):362–373, 1983. (Cited on pages 168, 169, and 172.)Google Scholar
[47] J., Arteche. Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models. Journal of Econometrics, 119(1):131–154, 2004. (Cited on page 611.)Google Scholar
[48] J., Arteche. Semiparametric inference in correlated long memory signal plus noise models. Econometric Reviews, 31(4):440–474, 2012. (Cited on page 611.)Google Scholar
[49] J., Arteche and J., Orbe. Bootstrap-based bandwidth choice for log-periodogram regression. Journal of Time Series Analysis, 30(6):591–617, 2009. (Cited on page 111.)Google Scholar
[50] J., Arteche and J., Orbe. Using the bootstrap for finite sample confidence intervals of the log periodogram regression. Computational Statistics & Data Analysis, 53(6):1940–1953, 2009. (Cited on page 111.)Google Scholar
[51] J., Arteche and P., M. Robinson. Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis, 21(1):1–25, 2000. (Cited on page 573.)Google Scholar
[52] R. B., Ash and M., F.|Gardner. Topics in Stochastic Processes. Probability and Mathematical Statistics, Vol. 27. New York, London: Academic Press [Harcourt Brace Jovanovich, Publishers], 1975. (Citedonpages 437 and 438.)
[53] A., Astrauskas. Limit theorems for sums of linearly generated random variables. Lithuanian Mathematical Journal, 23(2):127–134, 1983. (Cited on pages 82, 110, and 111.)Google Scholar
[54] A., Astrauskas, J. B., Levy, and M. S., Taqqu. The asymptotic dependence structure of the linear fractional Lévy motion. Lithuanian Mathematical Journal, 31(1):1–19, 1991. (Cited on pages 83 and 110.)Google Scholar
[55] K., Atkinson and W., Han. Spherical Harmonics and Approximations on the Unit Sphere: an Introduction, volume 2044 of Lecture Notes in Mathematics. Heidelberg: Springer, 2012. (Cited on pages 526 and 527.)
[56] M., Ausloos and D. H., Berman. A multivariate Weierstrass-Mandelbrot function. Proceedings of the Royal Society. London. Series A. Mathematical, Physical and Engineering Sciences, 400(1819):331–350, 1985. (Cited on page 227.)Google Scholar
[57] M., Avarucci and D., Marinucci. Polynomial cointegration between stationary processes with long memory. Journal of Time Series Analysis, 28(6):923–942, 2007. (Cited on page 537.)Google Scholar
[58] F., Avram. On bilinear forms in Gaussian random variables and Toeplitz matrices. Probability Theory and Related Fields, 79(1):37–45, 1988. (Cited on page 571.)Google Scholar
[59] F., Avram and M. S., Taqqu. Noncentral limit theorems and Appell polynomials. The Annals of Probability, 15:767–775, 1987. (Cited on page 343.)Google Scholar
[60] F., Avram, N., Leonenko and L., Sakhno. On a Szeg?o type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields. ESAIM. Probability and Statistics, 14:210–255, 2010. (Cited on page 571.)Google Scholar
[61] A., Ayache and W., Linde. Series representations of fractional Gaussian processes by trigonometric and Haar systems. Electronic Journal of Probability, 14:no. 94, 2691–2719, 2009. (Cited on page 465.)Google Scholar
[62] A., Ayache and M. S., Taqqu. Rate optimality of wavelet series approximations of fractional Brownian motion. The Journal of Fourier Analysis and Applications, 9(5):451–471, 2003. (Cited on page 465.)Google Scholar
[63] A., Ayache, S., Leger and M., Pontier. Drap brownien fractionnaire. Potential Analysis, 17(1):31–43, 2002. (Cited on page 537.)Google Scholar
[64] M., Azimmohseni, A. R., Soltani, and M., Khalafi. Simulation of real discrete time Gaussian multivariate stationary processes with given spectral densities. Journal of Time Series Analysis, 36(6):783–796, 2015. (Cited on page 112.)Google Scholar
[65] E., Azmoodeh, T., Sottinen, L., Viitasaari and A., Yazigi. Necessary and sufficient conditions for Hölder continuity of Gaussian processes. Statistics & Probability Letters, 94:230–235, 2014. (Cited on page 435.)Google Scholar
[66] F., Baccelli and A., Biswas. On scaling limits of power law shot-noise fields. Stochastic Models, 31(2):187–207, 2015. (Cited on page 225.)Google Scholar
[67] E., Bacry and J.-F., Muzy. Log-infinitely divisible multifractal processes. Communications in Mathematical Physics, 236(3):449–475, 2003. (Cited on page 612.)Google Scholar
[68] E., Bacry, J., Delour, and J.-F., Muzy. Multifractal random walk. Physical Review E, 64(2):026103, 2001. (Cited on page 612.)Google Scholar
[69] C., Baek and V., Pipiras. On distinguishing multiple changes in mean and long-range dependence using local Whittle estimation. Electronic Journal of Statistics, 8(1):931–964, 2014. (Cited on pages 225 and 573.)Google Scholar
[70] C., Baek, G., Didier and V., Pipiras. On integral representations of operator fractional Brownian fields. Statistics & Probability Letters, 92:190–198, 2014. (Cited on pages 537 and 538.)Google Scholar
[71] C., Baek, N., Fortuna and V., Pipiras. Can Markov switching model generate long memory? Economics Letters, 124(1):117–121, 2014. (Cited on pages 162 and 225.)Google Scholar
[72] C., Bahadoran, A., Benassi, and K., Dębicki. Operator-self-similar Gaussian processes with stationary increments. Preprint, 2003. (Cited on page 536.)Google Scholar
[73] L., Bai and J., Ma. Stochastic differential equations driven by fractional Brownian motion and Poisson point process. Bernoulli, 21(1):303–334, 2015. (Cited on page 436.)Google Scholar
[74] S., Bai and M., S. Taqqu. Multivariate limit theorems in the context of long-range dependence. Journal of Time Series Analysis, 34 (6): 717–743, 2013. (Cited on pages 320 and 344.)Google Scholar
[75] S., Bai and M. S., Taqqu. Multivariate limits of multilinear polynomial-form processes with long memory. Statistics & Probability Letters, 83(11):2473–2485, 2013. (Cited on pages 327 and 344.)Google Scholar
[76] S., Bai and M., S. Taqqu. Structure of the third moment of the generalized Rosenblatt distribution. Statistics & Probability Letters, 94:144–152, 2014. (Cited on page 344.)Google Scholar
[77] S., Bai and M.S., Taqqu. Generalized Hermite processes, discrete chaos and limit theorems. Stochastic Processes and their Applications, 124:1710–1739, 2014. (Cited on pages 276, 277, 281, and 344.)Google Scholar
[78] S., Bai and M. S., Taqqu. Convergence of long-memory discrete k-th order Volterra processes. Stochastic Processes and Their Applications, 125(5):2026–2053, 2015. (Cited on page 344.)Google Scholar
[79] S., Bai and M. S., Taqqu. The universality of homogeneous polynomial forms and critical limits. Journal of Theoretical Probability, 29(4):1710–1727, 2016. (Cited on page 344.)Google Scholar
[80] S., Bai and M. S., Taqqu. Short-range dependent processes subordinated to the Gaussian may not be strong mixing. Statistics & Probability Letters, 110:198–200, 2016. (Cited on page 612.)Google Scholar
[81] S., Bai and M. S., Taqqu. On the validity of resampling methods under long memory. To appear in The Annals of Statistics, 2017. (Cited on page 574.)
[82] S., Bai and M. S., Taqqu. The impact of diagonals of polynomial forms on limit theorems with long memory. Bernoulli, 23(1):710–742, 2017. (Cited on page 344.)Google Scholar
[83] S., Bai, M. S., Ginovyan, and M. S., Taqqu. Functional limit theorems for Toeplitz quadratic functionals of continuous time Gaussian stationary processes. Statistics & Probability Letters, 104:58–67, 2015. (Cited on page 571.)Google Scholar
[84] S., Bai, M. S., Ginovyan, and M. S., Taqqu. Limit theorems for quadratic forms of Lévy-driven continuous-time linear processes. Stochastic Processes and their Applications, 126(4):1036–1065, 2016. (Cited on page 571.)Google Scholar
[85] S., Bai, M. S., Taqqu, and T., Zhang. A unified approach to self-normalized block sampling. Stochastic Processes and their Applications, 126(8):2465–2493, 2016. (Cited on page 574.)Google Scholar
[86] R. T., Baillie and T., Bollerslev. Contintegration, fractional cointegration, and exchange rate dynamics. The Journal of Finance, 49:737–745, 1994. (Cited on page 537.)Google Scholar
[87] R. T., Baillie and G., Kapetanios. Testing for neglected nonlinearity in long-memory models. Journal of Business & Economic Statistics, 25(4):447–461, 2007. (Cited on page 611.)Google Scholar
[88] R. T., Baillie and G., Kapetanios. Estimation and inference for impulse response functions from univariate strongly persistent processes. The Econometrics Journal, 16(3):373–399, 2013. (Cited on page 573.)Google Scholar
[89] R. T., Baillie, T., Bollerslev and H. O., Mikkelsen. Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74(1):3–30, 1996. (Cited on page 611.)Google Scholar
[90] R. T., Baillie, G., Kapetanios and F., Papailias. Modified information criteria and selection of long memory time series models. Computational Statistics and Data Analysis, 76:116–131, 2014. (Cited on pages 552 and 572.)Google Scholar
[91] R. T., Baillie, G., Kapetanios and F., Papailias. Inference for impulse response coefficients from multivariate fractionally integrated processes. Econometric Reviews, 2016. (Cited on page 573.)
[92] R. M., Balan. Recent advances related to SPDEs with fractional noise. In R. C., Dalang, M., Dozzi, and F., Russo, editors, Seminar on Stochastic Analysis, Random Fields and Applications VII, volume 67 of Progress in Probability, pages 3–22. Basel: Springer, 2013. (Cited on page 227.)
[93] P., Balança. Some sample path properties of multifractional Brownian motion. Stochastic Processes and their Applications, 125(10):3823–3850, 2015. (Cited on page 611.)Google Scholar
[94] C., Barakat, P., Thiran, G., Iannaccone, C., Diot and P., Owezarski. Modeling Internet backbone traffic at the flow level. IEEE Transactions on Signal Processing, 51(8):2111–2124, 2003. (Cited on page 224.)Google Scholar
[95] Ph., Barbe and W. P., McCormick. Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution. Probab. Theory Related Fields, 154(3-4):429–476, 2012. (Cited on page 111.)Google Scholar
[96] J.-M., Bardet. Testing for the presence of self-similarity of Gaussian time series having stationary increments. Journal of Time Series Analysis, 21:497–515, 2000. (Cited on page 112.)Google Scholar
[97] J.-M., Bardet. Statistical study of the wavelet analysis of fractional Brownian motion. IEEE Transactions on Information Theory, 48:991–999, 2002. (Cited on page 112.)Google Scholar
[98] J.-M., Bardet and H., Bibi. Adaptive semiparametric wavelet estimator and goodness-of-fit test for long-memory linear processes. Electronic Journal of Statistics, 6:2383–2419, 2012. (Cited on page 112.)Google Scholar
[99] J.-M., Bardet, H., Bibi, and A., Jouini. Adaptive wavelet-based estimator of the memory parameter for stationary Gaussian processes. Bernoulli, 14(3):691–724, 2008. (Cited on page 112.)Google Scholar
[100] X., Bardina and K., Es-Sebaiy. An extension of bifractional Brownian motion. Communications on Stochastic Analysis, 5(2):333–340, 2011. (Cited on page 54.)Google Scholar
[101] O. E., Barndorff-Nielsen and N., N. Leonenko. Spectral properties of superpositions of OrnsteinUhlenbeck type processes. Methodology and Computing in Applied Probability, 7(3):335–352, 2005. (Cited on page 223.)Google Scholar
[102] J., Barral. Mandelbrot cascades and related topics. In Geometry and Analysis of Fractals, volume 88 of Springer Proc. Math. Stat., pages 1–45. Heidelberg: Springer, 2014. (Cited on page 612.)
[103] J., Barral and B., Mandelbrot. Multifractal products of cylindrical pulses. Probability Theory and Related Fields, 124(3):409–430, 2002. (Cited on page 612.)Google Scholar
[104] R. J., Barton and H. V., Poor. Signal detection in fractional Gaussian noise. IEEE Transactions on Information Theory, 34(5):943–959, 1988. (Cited on page 395.)Google Scholar
[105] G. K., Basak, N. H., Chan, and W., Palma. The approximation of long-memory processes by an arma model. Journal of Forecasting, 20(6):367–389, 2001. (Cited on page 571.)Google Scholar
[106] F., Baudoin and M., Hairer. A version of Hörmander's theorem for the fractional Brownian motion. Probability Theory and Related Fields, 139(3-4):373–395, 2007. (Cited on page 436.)Google Scholar
[107] F., Baudoin and C., Ouyang. Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions. Stochastic Processes and their Applications, 121(4):759–792, 2011. (Cited on page 436.)Google Scholar
[108] F., Baudoin, E., Nualart, C., Ouyang and S., Tindel. On probability laws of solutions to differential systems driven by a fractional Brownian motion. The Annals of Probability, 44(4):2554–2590, 2016. (Cited on page 436.)Google Scholar
[109] F., Baudoin, C., Ouyang and S., Tindel. Upper bounds for the density of solutions to stochastic differential equations driven by fractional Brownian motions. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 50(1):111–135, 2014. (Cited on page 436.)Google Scholar
[110] A., Baxevani and K., Podgórski. Lamperti transform and a series decomposition of fractional Brownian motion. Preprint, 2007. (Cited on page 465.)
[111] P., Becker-Kern and G., Pap. Parameter estimation of selfsimilarity exponents. Journal of Multivariate Analysis, 99(1):117–140, 2008. (Cited on page 536.)Google Scholar
[112] P., Becker-Kern, M. M., Meerschaert, and H.-P., Scheffler. Limit theorems for coupled continuous time random walks. The Annals of Probability, 32(1B):730–756, 2004. (Cited on page 227.)Google Scholar
[113] A., Benassi, S., Jaffard and D., Roux. Elliptic Gaussian random processes. Revista Matemática Iberoamericana, 13(1):19–90, 1997. (Cited on pages 145, 465, and 611.)Google Scholar
[114] A., Benassi, S., Cohen and J., Istas. Identifying the multifractional function of a Gaussian process. Statistics & Probability Letters, 39(4):337–345, 1998. (Cited on page 611.)Google Scholar
[115] A., Benassi, S., Cohen and J., Istas. Identification and properties of real harmonizable fractional Lévy motions. Bernoulli, 8(1):97–115, 2002. (Cited on page 145.)Google Scholar
[116] C., Bender. An S-transform approach to integration with respect to a fractional Brownian motion. Bernoulli, 9(6):955–983, 2003. (Cited on page 435.)Google Scholar
[117] C., Bender. An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter. Stochastic Processes and their Applications, 104(1):81–106, 2003. (Cited on page 435.)Google Scholar
[118] C., Bender, T., Sottinen and E., Valkeila. Arbitrage with fractional Brownian motion? Theory of Stochastic Processes, 13(1-2):23–34, 2007. (Cited on page 435.)Google Scholar
[119] D. A., Benson, M. M., Meerschaert, B., Baeumer, and H.-P., Scheffler. Aquifer operator scaling and the effect on solute mixing and dispersion. Water Resources Research, 42(1):W01415, 2006. (Cited on page 537.)Google Scholar
[120] J., Beran. A goodness of fit test for time series with long-range dependence. Journal of the Royal Statistical Society, Series B, 54:749–760, 1992. (Cited on page 554.)Google Scholar
[121] J., Beran. Statistics for Long-Memory Processes. New York: Chapman & Hall, 1994. (Cited on pages 109 and 572.)
[122] J., Beran. Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models. Journal of the Royal Statistical Society. Series B. Methodological, 57(4):659–672, 1995. (Cited on page 551.)Google Scholar
[123] J., Beran and Y., Feng. SEMIFAR models—a semiparametric approach to modelling trends, long-range dependence and nonstationarity. Computational Statistics & Data Analysis, 40(2):393–419, 2002. (Cited on page 573.)Google Scholar
[124] J., Beran, R. J., Bhansali, and D., Ocker. On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes. Biometrika, 85(4):921–934, 1998. (Cited on page 552.)Google Scholar
[125] J., Beran, S., Ghosh and D., Schell. On least squares estimation for long-memory lattice processes. Journal of Multivariate Analysis, 100(10):2178–2194, 2009. (Cited on pages 529 and 537.)Google Scholar
[126] J., Beran, M., Schützner, and S., Ghosh. From short to long memory: aggregation and estimation. Computational Statistics and Data Analysis, 54(11):2432–2442, 2010. (Cited on page 223.)Google Scholar
[127] J., Beran, Y., Feng, S., Ghosh and R., Kulik. Long-Memory Processes: Probabilistic Properties and Statistical Methods. Springer, 2013. (Cited on pages 109, 539, 545, 551, 573, 574, and 610.)
[128] J., Beran, S., Möhrle, and S., Ghosh. Testing for Hermite rank in Gaussian subordination processes. Journal of Computational and Graphical Statistics, 2016. (Cited on page 343.)
[129] C., Berg. The cube of a normal distribution is indeterminate. The Annals of Probability, 16(2):910– 913, 1988. (Cited on page 280.)Google Scholar
[130] I., Berkes, L., Horváth, P., Kokoszka, and Q.-M., Shao. On discriminating between long-range dependence and changes in mean. The Annals of Statistics, 34(3):1140–1165, 2006. (Cited on pages 225 and 573.)Google Scholar
[131] S. M., Berman. Local nondeterminism and local times of Gaussian processes. Indiana University Mathematics Journal, 23:69–94, 1973/74. (Cited on page 430.)Google Scholar
[132] S. M., Berman. High level sojourns for strongly dependent Gaussian processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 50:223–236, 1979. (Cited on page 343.)Google Scholar
[133] S. M., Berman. Sojourns of vector Gaussian processes inside and outside spheres. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 66:529–542, 1984. (Cited on page 344.)Google Scholar
[134] S. M., Berman. Sojourns and Extremes of Stochastic Processes. The Wadsworth & Brooks/Cole Statistics/Probability Series. Pacific Grove, CA: Wadsworth & Brooks/Cole Advanced Books & Software, 1992. (Cited on page 178.)
[135] M. V., Berry and Z.V., Lewis. On the Weierstrass-Mandelbrot fractal function. Proceedings of the Royal Society of London, A370:459–484, 1980. (Cited on page 227.)Google Scholar
[136] S., Bertelli and M., Caporin. A note on calculating autocovariances of long-memory processes. Journal of Time Series Analysis, 23(5):503–508, 2002. (Cited on pages 539 and 570.)Google Scholar
[137] J., Bertoin and I., Kortchemski. Self-similar scaling limits of Markov chains on the positive integers. The Annals of Applied Probability, 26(4):2556–2595, 2016. (Cited on page 612.)Google Scholar
[138] C., Berzin, A., Latour and J. R., León. Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion. Lecture Notes in Statistics. Springer International Publishing, 2014. (Cited on page 610.)
[139] A., Beskos, J., Dureau and K., Kalogeropoulos. Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion. Biometrika, 102(4):809–827, 2015. (Citedonpage 436.)Google Scholar
[140] A., Betken and M., Wendler. Subsampling for general statistics under long range dependence. Preprint, 2015. (Cited on page 574.)
[141] R. J., Bhansali and P. S., Kokoszka. Estimation of the long-memory parameter: a review of recent developments and an extension. In selected Proceedings of the Symposium on Inference for Stochastic Processes (Athens, GA, 2000), volume 37 of IMS Lecture Notes Monogr. Ser., pages 125–150. Beachwood, OH: Inst. Math. Statist., 2001. (Cited on page 571.)
[142] R. J., Bhansali and P. S., Kokoszka. Computation of the forecast coefficients for multistep prediction of long-range dependent time series. International Journal of Forecasting, 18(2):181–206, 2002. (Cited on page 571.)Google Scholar
[143] R. J., Bhansali and P. S., Kokoszka. Prediction of long-memory time series. In Theory and Applications of Long-Range Dependence, pages 355–367. Boston, MA: Birkhäuser Boston, 2003. (Cited on page 571.)
[144] R. J., Bhansali, L., Giraitis and P. S., Kokoszka. Estimation of the memory parameter by fitting fractionally differenced autoregressive models. Journal of Multivariate Analysis, 97(10):2101–2130, 2006. (Cited on page 573.)Google Scholar
[145] G., Bhardwaj and N. R., Swanson. An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series. Journal of Econometrics, 131(1-2):539– 578, 2006. (Cited on page 571.)Google Scholar
[146] F., Biagini, B., Øksendal, A., Sulem, and N., Wallner. An introduction to white-noise theory and Malliavin calculus for fractional Brownian motion. Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 460(2041):347–372, 2004. Stochastic analysis with applications to mathematical finance. (Cited on pages 435 and 610.)Google Scholar
[147] F., Biagini, Y., Hu, B., Øksendal, and T., Zhang. Stochastic Calculus for Fractional Brownian Motion and Applications. Probability and its Applications (New York). London: Springer-Verlag London, Ltd., 2008. (Cited on page 436.)
[148] H., Biermé and A., Estrade. Poisson random balls: self-similarity and X-ray images. Advances in Applied Probability, 38(4):853–872, 2006. (Cited on page 224.)Google Scholar
[149] H., Biermé and F., Moisan, L., and Richard, . A turning-band method for the simulation of anisotropic fractional Brownian fields. Journal of Computational and Graphical Statistics, 24(3):885–904, 2015. (Cited on page 112.)Google Scholar
[150] H., Biermé and F., Richard. Estimation of anisotropic Gaussian fields through Radon transform. ESAIM. Probability and Statistics, 12:30–50 (electronic), 2008. (Cited on page 529.)Google Scholar
[151] H., Biermé, M. M., Meerschaert, and H.-P., Scheffler. Operator scaling stable random fields. Stochastic Processes and their Applications, 117(3):312–332, 2007. (Cited on pages 511, 512, 521, 522, 535, 536, and 537.)Google Scholar
[152] H., Biermé, C., Lacaux, and H.-P., Scheffler. Multi-operator scaling random fields. Stochastic Processes and their Applications, 121(11):2642–2677, 2011. (Cited on page 537.)Google Scholar
[153] H., Biermé, O., Durieu, and Y., Wang. Invariance principles for operator-scaling Gaussian random fields. To appear in The Annals of Applied Probability. Preprint, 2015. (Cited on page 226.)
[154] P., Billingsley. Convergence of Probability Measures, 2nd edition. Wiley Series in Probability and Statistics: Probability and Statistics. New York: John Wiley & Sons Inc., 1999. A Wiley-Interscience Publication. (Cited on pages 219, 292, 296, 583, and 584.)
[155] N. H., Bingham. Szegö's theorem and its probabilistic descendants. Probability Surveys, 9:287–324, 2012. (Cited on page 571.)Google Scholar
[156] N. H., Bingham. Multivariate prediction and matrix Szegö theory. Probability Surveys, 9:325–339, 2012. (Cited on page 571.)Google Scholar
[157] N. H., Bingham, C. M., Goldie, and J. L., Teugels. Regular Variation, volume 27 of Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press, 1987. (Cited on pages 17, 19, 20, 25, 70, 109, 130, 176, 527, 582, and 586.)
[158] L., Bisaglia. Model selection for long-memory models. Quaderni di Statistica, 4:33–49, 2002. (Cited on page 571.)Google Scholar
[159] L., Bisaglia and M., Gerolimetto. An empirical strategy to detect spurious effects in long memory and occasional-break processes. Communications in Statistics - Simulation and Computation, 38:172–189, 2009. (Cited on page 573.)Google Scholar
[160] L., Bisaglia and D., Guégan. A comparison of techniques of estimation in long-memory processes. Computational Statistics and Data Analysis, 27:61–81, 1998. (Cited on page 571.)Google Scholar
[161] L., Bisaglia, S., Bordignon and N., Cecchinato. Bootstrap approaches for estimation and confidence intervals of long memory processes. Journal of Statistical Computation and Simulation, 80(9-10):959–978, 2010. (Cited on page 573.)Google Scholar
[162] J., Blath, A., González Casanova, N., Kurt, and D., Spanò. The ancestral process of long-range seed bank models. Journal of Applied Probability, 50(3):741–759, 2013. (Cited on page 226.)Google Scholar
[163] T., Blu and M., Unser. Self-similarity. II. Optimal estimation of fractal processes. IEEE Transactions on Signal Processing, 55(4):1364–1378, 2007. (Cited on page 465.)Google Scholar
[164] P., Bocchinia and G., Deodatis. Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields. Probabilistic Engineering Mechanics, 23:393–407, 2008. (Cited on page 344.)Google Scholar
[165] D. C., Boes and J. D., Salas. Nonstationarity of the mean and the Hurst phenomenon. Water Resourses Research, 14(1):135–143, 1978. (Cited on page 225.)Google Scholar
[166] L. V., Bogachev. Random walks in random environments. In J.-P., Francoise, G., Naber, and S. T., Tsou, editors, Encyclopedia of Mathematical Physics, volume 4, pages 353–371. Oxford: Elsevier, 2006. (Cited on page 178.)
[167] V. I., Bogachev. Gaussian Measures, volume 62 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society, 1998. (Cited on pages 409 and 422.)
[168] Y., Boissy, B. B., Bhattacharyya, X., Li, and G. D., Richardson. Parameter estimates for fractional autoregressive spatial processes. The Annals of Statistics, 33(6):2553–2567, 2005. (Cited on pages 529 and 537.)Google Scholar
[169] T., Bojdecki and A., Talarczyk. Particle picture interpretation of some Gaussian processes related to fractional Brownian motion. Stochastic Processes and their Applications, 122(5):2134–2154, 2012. (Cited on page 228.)Google Scholar
[170] T., Bojdecki, L. G., Gorostiza, and A., Talarczyk. Limit theorems for occupation time fluctuations of branching systems. I. Long-range dependence. Stochastic Processes and their Applications, 116(1):1–18, 2006. (Cited on page 228.)Google Scholar
[171] T., Bojdecki, L. G., Gorostiza, and A., Talarczyk. Limit theorems for occupation time fluctuations of branching systems. II. Critical and large dimensions. Stochastic Processes and their Applications, 116(1):19–35, 2006. (Cited on page 228.)Google Scholar
[172] T., Bojdecki, L. G., Gorostiza, and A., Talarczyk. From intersection local time to the Rosenblatt process. Journal of Theoretical Probability, 28(3):1227–1249, 2015. (Cited on page 228.)Google Scholar
[173] A., Bonami and A., Estrade. Anisotropic analysis of some Gaussian models. The Journal of Fourier Analysis and Applications, 9(3):215–236, 2003. (Cited on page 529.)Google Scholar
[174] P., Bondon and W., Palma. A class of antipersistent processes. Journal of Time Series Analysis, 28(2):261–273, 2007. (Cited on page 109.)Google Scholar
[175] A., Borodin and I., Corwin. Macdonald processes. Probability Theory and Related Fields, 158(1-2):225–400, 2014. (Cited on page 227.)Google Scholar
[176] A., Böttcher and B., Silbermann. Toeplitz matrices and determinants with Fisher-Hartwig symbols. Journal of Functional Analysis, 63(2):178–214, 1985. (Cited on page 211.)Google Scholar
[177] J.-P., Bouchaud and A., Georges. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Physics Reports, 195(4-5):127–293, 1990. (Cited on page 227.)Google Scholar
[178] J.-P., Bouchaud, A., Georges, J., Koplik, A., Provata, and S., Redner. Superdiffusion in random velocity fields. Physical Review Letters, 64(21):2503, 1990. (Cited on page 226.)Google Scholar
[179] M., Boutahar, V., Marimoutou and L., Nouira. Estimation methods of the long memory parameter: Monte Carlo analysis and application. Journal of Applied Statistics, 34(3-4):261–301, 2007. (Cited on page 571.)Google Scholar
[180] C., Boutillier and B., de Tilière. The critical Z-invariant Ising model via dimers: the periodic case. Probability Theory and Related Fields, 147(3-4):379–413, 2010. (Cited on page 227.)Google Scholar
[181] R. C., Bradley. Basic properties of strong mixing conditions. A survey and some open questions. Probability Surveys, 2:107–144, 2005. ISSN 1549-5787. Update of, and a supplement to, the 1986 original. (Cited on page 612.)Google Scholar
[182] M., Bramson and D., Griffeath. Renormalizing the 3-dimensional voter model. The Annals of Probability, 7(3):418–432, 1979. (Cited on page 226.)Google Scholar
[183] J.-C., Breton and I., Nourdin. Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion. Electronic Communications in Probability, 13:482–493, 2008. (Cited on page 281.)Google Scholar
[184] P., Breuer and P., Major. Central limit theorems for non-linear functionals of Gaussian fields. Journal of Multivariate Analysis, 13:425–441, 1983. (Cited on pages 282, 343, and 344.)Google Scholar
[185] D. R., Brillinger. Time Series, volume 36 of Classics in Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2001. Data Analysis and Theory, Reprint of the 1981 edition. (Cited on page 470.)
[186] P. J., Brockwell and R. A., Davis. Time Series: Theory and Methods, 2nd edition. New York: Springer Series in Statistics. Springer-Verlag, 1991. (Cited on pages xxi, 9, 14, 28, 32, 33, 37, 39, 109, 337, 470, 471, 497, 500, 541, 544, 552, and 554.)
[187] J., Brodsky and C., M. Hurvich. Multi-step forecasting for long-memory processes. Journal of Forecasting, 18:59–75, 1999. (Cited on page 571.)Google Scholar
[188] J. C., Bronski. Asymptotics of Karhunen-Loeve eigenvalues and tight constants for probability distributions of passive scalar transport. Communications in Mathematical Physics, 238(3):563–582, 2003. (Cited on page 464.)Google Scholar
[189] J. C., Bronski. Small ball constants and tight eigenvalue asymptotics for fractional Brownian motions. Journal of Theoretical Probability, 16(1):87–100, 2003. (Cited on page 464.)Google Scholar
[190] A., Brouste and M., Kleptsyna. Asymptotic properties of MLE for partially observed fractional diffusion system. Statistical Inference for Stochastic Processes, 13(1):1–13, 2010. (Cited on page 395.)Google Scholar
[191] A., Brouste, J., Istas, and S., Lambert-Lacroix. On fractional Gaussian random fields simulations. Journal of Statistical Software, 23(1):1–23, 2007. (Cited on page 112.)Google Scholar
[192] B., Buchmann and C., Klüppelberg. Fractional integral equations and state space transforms. Bernoulli, 12(3):431–456, 2006. (Cited on page 436.)Google Scholar
[193] A., Budhiraja, V., Pipiras and X., Song. Admission control for multidimensional workload input with heavy tails and fractional Ornstein-Uhlenbeck process. Advances in Applied Probability, 47:1–30, 2015. (Cited on page 224.)Google Scholar
[194] K., Burnecki and G., Sikora. Estimation of FARIMA parameters in the case of negative memory and stable noise. IEEE Transactions on Signal Processing, 61(11):2825–2835, 2013. (Cited on pages 111 and 573.)Google Scholar
[195] K., Burnecki, M., Maejima and A., Weron. The Lamperti transformation for self-similar processes. Yokohama Mathematical Journal, 44(1):25–42, 1997. (Cited on page 111.)Google Scholar
[196] M., Çağlar. A long-range dependent workload model for packet data traffic. Mathematics of Operations Research, 29(1):92–105, 2004. (Cited on page 224.)Google Scholar
[197] M., Calder and R., A. Davis. Introduction to Whittle (1953) “The Analysis of Multiple Stationary Time Series”. In S., Kotz and N. L., Johnson, editors, Breakthroughs in Statistics, volume 3, pages 141–148. Springer-Verlag, 1997. (Cited on page 570.)
[198] F., Camia, C., Garban and C. M., Newman. Planar Ising magnetization field I. Uniqueness of the critical scaling limit. The Annals of Probability, 43(2):528–571, 2015. (Cited on page 227.)Google Scholar
[199] F., Camia, C., Garban and C. M., Newman. Planar Ising magnetization field II. Properties of the critical and near-critical scaling limits. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 52(1):146–161, 2016. (Cited on page 227.)Google Scholar
[200] B., Candelpergher, M., Miniconi and F., Pelgrin. Long-memory process and aggregation of AR(1) stochastic processes: A new characterization. Preprint, 2015. (Cited on page 224.)
[201] G. M., Caporale, J., Cuñado, and L. A., Gil-Alana. Modelling long-run trends and cycles in financial time series data. Journal of Time Series Analysis, 34(3):405–421, 2013. (Cited on page 110.)Google Scholar
[202] K. A. E., Carbonez. Model selection and estimation of long-memory time-series models. Review of Business and Economics, XLIV(4):512–554, 2009. (Cited on page 571.)Google Scholar
[203] P., Carmona, L., Coutin and G., Montseny. Stochastic integration with respect to fractional Brownian motion. Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 39(1):27–68, 2003. (Cited on page 435.)Google Scholar
[204] K. J. E., Carpio and D. J., Daley. Long-range dependence of Markov chains in discrete time on countable state space. Journal of Applied Probability, 44(4):1047–1055, 2007. (Cited on page 109.)Google Scholar
[205] T., Cass and P., Friz. Densities for rough differential equations under Hörmander's condition. Annals of Mathematics. Second Series, 171(3):2115–2141, 2010. (Cited on page 436.)Google Scholar
[206] T., Cass, M., Hairer, C., Litterer and S., Tindel. Smoothness of the density for solutions to Gaussian rough differential equations. The Annals of Probability, 43(1):188–239, 2015. (Cited on page 436.)Google Scholar
[207] A., Castaño-Martínez and F., López-Blázquez. Distribution of a sum of weighted noncentral chi-square variables. Test, 14(2):397–415, 2005. (Cited on page 271.)Google Scholar
[208] D., Celov, R., Leipus and A., Philippe. Time series aggregation, disaggregation, and long memory. Lietuvos Matematikos Rinkinys, 47(4):466–481, 2007. (Cited on pages 117, 221, and 223.)Google Scholar
[209] D., Chambers and E., Slud. Central limit theorems for nonlinear functionals of stationary Gaussian processes. Probability Theory and Related Fields, 80:323–346, 1989. (Cited on page 343.)Google Scholar
[210] D., Chambers and E., Slud. Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems. Stochastic Processes and their Applications, 32(1):93–107, 1989. (Cited on page 343.)Google Scholar
[211] M. J., Chambers. The simulation of random vector time series with given spectrum. Mathematical and Computer Modelling, 22(2):1–6, 1995. (Cited on page 112.)Google Scholar
[212] M. J., Chambers. Long memory and aggregation in macroeconomic time series. International Economic Review, 39(4):1053–1072, 1998. Symposium on Forecasting and Empirical Methods in Macroeconomics and Finance. (Cited on page 223.)Google Scholar
[213] G., Chan and A. T. A., Wood. An algorithm for simulating stationary Gaussian random fields. Applied Statistics, Algorithm Section, 46:171–181, 1997. (Cited on page 112.)Google Scholar
[214] G., Chan and A. T. A., Wood. Simulation of stationary Gaussian vector fields. Statistics and Computing, 9(4):265–268, 1999. (Cited on page 112.)Google Scholar
[215] N. H., Chan and W., Palma. State space modeling of long-memory processes. The Annals of Statistics, 26(2):719–740, 1998. (Cited on page 573.)Google Scholar
[216] C., Chen and L., Yan. Remarks on the intersection local time of fractional Brownian motions. Statistics & Probability Letters, 81(8):1003–1012, 2011. (Cited on page 436.)Google Scholar
[217] L.-C., Chen and A., Sakai. Critical two-point functions for long-range statistical-mechanical models in high dimensions. The Annals of Probability, 43(2):639–681, 2015. (Cited on page 227.)Google Scholar
[218] L. H. Y., Chen, L., Goldstein, and Q.-M., Shao. Normal Approximation by Stein's Method. Probability and its Applications (New York). Heidelberg: Springer, 2011. (Cited on page 426.)
[219] W. W., Chen. Efficiency in estimation of memory. Journal of Statistical Planning and Inference, 140(12):3820–3840, 2010. (Cited on page 572.)Google Scholar
[220] W. W., Chen and R., S.|Deo. A generalized Portmanteau goodness-of-fit test for time series models. Econometric Theory, 20(2):382–416, 2004. (Cited on page 553.)Google Scholar
[221] W. W., Chen and R., S. Deo. Estimation of mis-specified long memory models. Journal of Econometrics, 134(1):257–281, 2006. ISSN 0304-4076. (Cited on page 571.)Google Scholar
[222] W. W., Chen and C. M., Hurvich. Semiparametric estimation of multivariate fractional cointegration. Journal of the American Statistical Association, 98(463):629–642, 2003. (Cited on page 537.)Google Scholar
[223] W. W., Chen and C., M. Hurvich. Semiparametric estimation of fractional cointegrating subspaces. The Annals of Statistics, 34(6):2939–2979, 2006. (Cited on page 537.)Google Scholar
[224] W. W., Chen, C. M., Hurvich, and Y., Lu. On the correlation matrix of the discrete Fourier transform and the fast solution of large Toeplitz systems for long-memory time series. Journal of the American Statistical Association, 101(474):812–822, 2006. (Cited on page 570.)Google Scholar
[225] X., Chen, W. V., Li, J., Rosiński, and Q.-M., Shao. Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. The Annals of Probability, 39(2):729–778, 2011. (Cited on page 436.)Google Scholar
[226] Z., Chen, L., Xu and D., Zhu. Generalized continuous time random walks and Hermite processes. Statistics & Probability Letters, 99:44–53, 2015. (Cited on page 228.)
[227] P., Cheridito. Arbitrage in fractional Brownian motion models. Finance and Stochastics, 7(4):533– 553, 2003. (Cited on page 435.)Google Scholar
[228] P., Cheridito and D., Nualart. Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H ∈ (0, 1 2). Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 41(6):1049–1081, 2005. (Cited on pages 406, 433, and 435.)Google Scholar
[229] P., Cheridito, H., Kawaguchi and M., Maejima. Fractional Ornstein-Uhlenbeck processes. Electronic Journal of Probability, 8:no. 3, 14 pp. (electronic), 2003. (Cited on pages 384 and 394.)Google Scholar
[230] Y.-W., Cheung. Long memory in foreign exchange rates. Journal of Business and Economic Statistics, 11:93–101, 1993. (Cited on page 572.)Google Scholar
[231] Y.-W., Cheung and F. X., Diebold. On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean. Journal of Econometrics, 62:301–316, 1994. (Citedonpage 571.)Google Scholar
[232] Y.-W., Cheung and K. S., Lai. A fractional cointegration analysis of purchasing power parity. Journal of Business & Economic Statistics, 11(1):103–112, 1993. (Cited on page 537.)Google Scholar
[233] G., Chevillon and S., Mavroeidis. Learning can generate long memory. To appear in Journal of Econometrics. Preprint, 2013. (Cited on page 228.)
[234] Z., Chi. Construction of stationary self-similar generalized fields by random wavelet expansion. Probability Theory and Related Fields, 121(2):269–300, 2001. (Cited on page 465.)Google Scholar
[235] P., Chigansky and M., Kleptsyna. Spectral asymptotics of the fractional Brownian covariance operator. Preprint, 2015. (Cited on page 440.)
[236] P., Chigansky and M., Kleptsyna. Asymptotics of the Karhunen-Loève expansion for the fractional Brownian motion. Preprint, 2016. (Cited on page 439.)
[237] J.-P., Chilès and P., Delfiner. Geostatistics, 2nd edition. Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons Inc., 2012. Modeling spatial uncertainty. (Cited on page 538.)
[238] B. J., Christensen and M., Ø Nielsen. Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting. Journal of Econometrics, 133(1):343–371, 2006. (Cited on page 536.)Google Scholar
[239] A., Chronopoulou and S., Tindel. On inference for fractional differential equations. Statistical Inference for Stochastic Processes, 16(1):29–61, 2013. (Cited on page 436.)Google Scholar
[240] A., Chronopoulou, C. A., Tudor, and F. G., Viens. Application of Malliavin calculus to long-memory parameter estimation for non-Gaussian processes. Comptes Rendus Mathématique. Académie des Sciences. Paris, 347(11-12):663–666, 2009. (Cited on page 281.)Google Scholar
[241] A., Chronopoulou, C. A., Tudor, and F. G., Viens. Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes. Communications on Stochastic Analysis, 5(1):161–185, 2011. (Cited on page 281.)Google Scholar
[242] C.-F., Chung. A note on calculating the autocovariances of the fractionally integrated ARMA models. Economics Letters, 45(3):293–297, 1994. (Cited on pages 539 and 570.)Google Scholar
[243] Z., Ciesielski, G., Kerkyacharian and B., Roynette. Quelques espaces fonctionnels associés à des processus gaussiens. Studia Mathematica, 107(2):171–204, 1993. (Cited on page 435.)Google Scholar
[244] R., Cioczek-Georges and B. B., Mandelbrot. Alternative micropulses and fractional Brownian motion. Stochastic Processes and their Applications, 64:143–152, 1996. (Cited on page 224.)Google Scholar
[245] B., Cipra. Statistical physicists phase out a dream. Science, 288(5471):1561–1562, 2000. (Cited on page 181.)Google Scholar
[246] M., Clausel. Gaussian fields satisfying simultaneous operator scaling relations. In Recent Developments in Fractals and Related Fields, Appl. Numer. Harmon. Anal., pages 327–341. Boston, MA: Birkhäuser Boston Inc., 2010. (Cited on page 537.)
[247] M., Clausel and B., Vedel. Explicit construction of operator scaling Gaussian random fields. Fractals, 19(1):101–111, 2011. (Cited on page 537.)Google Scholar
[248] M., Clausel, F., Roueff, M. S., Taqqu, and C., Tudor. Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory. Applied and Computational Harmonic Analysis, 32(2):223–241, 2012. (Cited on page 112.)Google Scholar
[249] M., Clausel, F., Roueff, M. S., Taqqu, and C., Tudor. High order chaotic limits of wavelet scalograms under long-range dependence. ALEA-Latin American Journal of Probability and Mathematical Statistics, 10(2):979–1011, 2013. (Cited on page 112.)Google Scholar
[250] M., Clausel, F., Roueff, M. S., Taqqu, and C., Tudor. Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes. ESAIM: Probability and Statistics, 18:42–76, 2014. (Cited on page 112.)Google Scholar
[251] J.-F., Coeurjolly. Identification of multifractional Brownian motion. Bernoulli, 11(6):987–1008, 2005. (Cited on page 611.)Google Scholar
[252] J.-F., Coeurjolly, P.-O., Amblard, and S., Achard. Wavelet analysis of the multivariate fractional Brownian motion. ESAIM. Probability and Statistics, 17:592–604, 2013. (Cited on page 536.)Google Scholar
[253] S., Cohen and J., Istas. Fractional Fields and Applications, volume 73 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Heidelberg: Springer, 2013. With a foreword by S., Jaffard. (Cited on pages 65, 110, 537, and 610.)
[254] S., Cohen and G., Samorodnitsky. Random rewards, fractional Brownian local times and stable self-similar processes. The Annals of Applied Probability, 16(3):1432–1461, 2006. (Cited on page 226.)Google Scholar
[255] S., Cohen, M. M., Meerschaert, and J., Rosiński. Modeling and simulation with operator scaling. Stochastic Processes and their Applications, 120(12):2390–2411, 2010. (Cited on page 536.)Google Scholar
[256] S., Cohen, F., Panloup and S., Tindel. Approximation of stationary solutions to SDEs driven by multiplicative fractional noise. Stochastic Processes and their Applications, 124(3):1197–1225, 2014. (Cited on page 436.)Google Scholar
[257] F., Comte and E., Renault. Long memory in continuous-time stochastic volatility models. Mathematical Finance, 8(4):291–323, 1998. (Cited on page 611.)Google Scholar
[258] P. L., Conti, L., De Giovanni, S. A., Stoev, and M. S., Taqqu. Confidence intervals for the long memory parameter based on wavelets and resampling. Statistica Sinica, 18(2):559–579, 2008. (Cited on page 573.)Google Scholar
[259] J., Contreras-Reyes, G. M., Goerg, and W., Palma. R package afmtools: Estimation, Diagnostic and Forecasting Functions for ARFIMA models (version 0.1.7). Chile: Universidad de Chile, 2011. URL http://cran.r-project.org/web/packages/afmtools. (Citedonpage 572.)
[260] D., Conus, M., Joseph, D., Khoshnevisan, and S.-Y., Shiu. Initial measures for the stochastic heat equation. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 50(1):136–153, 2014. (Cited on page 227.)Google Scholar
[261] J. B., Conway. A Course in Functional Analysis, 2nd edition, volume 96 of Graduate Texts in Mathematics. New York: Springer-Verlag, 1990. (Cited on page 260.)
[262] L., Coutin and L., Decreusefond. Abstract nonlinear filtering theory in the presence of fractional Brownian motion. The Annals of Applied Probability, 9(4): 1058–1090, 1999. (Cited on page 436.)Google Scholar
[263] L., Coutin and Z., Qian. Stochastic analysis, rough path analysis and fractional Brownian motions. Probability Theory and Related Fields, 122(1):108–140, 2002. (Cited on page 435.)Google Scholar
[264] L., Coutin, D., Nualart and C. A., Tudor. Tanaka formula for the fractional Brownian motion. Stochastic Processes and their Applications, 94(2):301–315, 2001. (Cited on pages 432 and 433.)Google Scholar
[265] D. R., Cox. Long-range dependence: a review. In H.A., David and H.T., David, editors, Statistics: An Appraisal, pages 55–74. Iowa State University Press, 1984. (Cited on page 225.)
[266] D.R., Cox and M.W., Townsend. The use of correlograms for measuring yarn irregularity. Journal of the Textile Institute Proceedings, 42(4):P145–P151, 1951. (Cited on pages 109 and 225.)Google Scholar
[267] P. F., Craigmile. Simulating a class of stationary Gaussian processes using the Davies-Harte algorithm, with application to long memory processes. Journal of Time Series Analysis, 24(5):505–511, 2003. (Cited on page 112.)Google Scholar
[268] P. F., Craigmile, P., Guttorp and D. B., Percival. Wavelet-based parameter estimation for polynomial contaminated fractionally differenced processes. IEEE Transactions on Signal Processing, 53(8, part 2):3151–3161, 2005. (Cited on page 112.)Google Scholar
[269] N., Crato and B. K., Ray. Model selection and forecasting for long-range dependent processes. Journal of Forecasting, 15:107–125, 1996. (Cited on page 552.)Google Scholar
[270] M. E., Crovella and A., Bestavros. Self-similarity in World Wide Web traffic: evidence and possible causes. IEEE/ACM Transactions on Networking, 5(6):835–846, 1997. (Cited on page 121.)Google Scholar
[271] J. D., Cryer and K. S., Chan. Time Series Analysis: With Applications in R. Springer Texts in Statistics. Springer, 2008. (Cited on page 14.)
[272] J., Cuzick. A central limit theorem for the number of zeros of a stationary Gaussian process. The Annals of Probability, 4(4):547–556, 1976. (Cited on page 343.)Google Scholar
[273] C., Czichowsky and W., Schachermayer. Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion. To appear in The Annals of Applied Probability. Preprint, 2015. (Cited on page 435.)
[274] D., Dacunha-Castelle and L., Fermín. Disaggregation of long memory processes on C∞ class. Electronic Communications in Probability, 11:35–44 (electronic), 2006. (Cited on page 223.)Google Scholar
[275] D., Dacunha-Castelle and L., Fermín. Aggregation of autoregressive processes and long memory. Preprint, 2008. (Cited on page 223.)
[276] D., Dacunha-Castelle and G., Oppenheim. Mixtures, aggregation and long memory. Preprint, 2001. (Citedonpage 223.)
[277] R., Dahlhaus. Efficient parameter estimation for self similar processes. The Annals of Statistics, 17(4):1749–1766, 1989. (Cited on pages 540, 546, and 571.)Google Scholar
[278] R., Dahlhaus. Correction: Efficient parameter estimation for self-similar processes. The Annals of Statistics, 34(2):1045–1047, 2006. (Cited on pages 540, 546, and 571.)Google Scholar
[279] H., Dai. Convergence in law to operator fractional Brownian motions. Journal of Theoretical Probability, 26(3):676–696, 2013. (Cited on page 536.)Google Scholar
[280] W., Dai and C. C., Heyde. Itô's formula with respect to fractional Brownian motion and its application. Journal of Applied Mathematics and Stochastic Analysis, 9(4):439–448, 1996. (Cited on page 435.)Google Scholar
[281] D. J., Daley. The Hurst index of long-range dependent renewal processes. The Annals of Probability, 27(4):2035–2041, 1999. (Cited on page 610.)Google Scholar
[282] D. J., Daley and D., Vere-Jones. An Introduction to the Theory of Point Processes. Vol. I, 2nd edition. Probability and its Applications (New York). New York: Springer-Verlag, 2003. Elementary Theory and Methods. (Cited on page 610.)
[283] D. J., Daley and D., Vere-Jones. An Introduction to the Theory of Point Processes. Vol. II, 2nd edition. Probability and its Applications (New York). New York: Springer, 2008. General theory and structure. (Cited on page 610.)
[284] D. J., Daley and R., Vesilo. Long range dependence of point processes, with queueing examples. Stochastic Processes and their Applications, 70(2):265–282, 1997. (Cited on page 610.)Google Scholar
[285] D. J., Daley, T., Rolski and R., Vesilo. Long-range dependent point processes and their Palm-Khinchin distributions. Advances in Applied Probability, 32(4):1051–1063, 2000. (Cited on page 610.)Google Scholar
[286] J., Damarackas and V., Paulauskas. Properties of spectral covariance for linear processes with infinite variance. Lithuanian Mathematical Journal, 54(3):252–276, 2014. (Cited on page 111.)Google Scholar
[287] I., Daubechies. Ten Lectures on Wavelets. SIAM Philadelphia, 1992. CBMS-NSF series, Volume 61. (Cited on pages 444 and 451.)
[288] B., D'Auria and S. I., Resnick. The influence of dependence on data network models. Advances in Applied Probability, 40(1):60–94, 2008. (Cited on page 224.)Google Scholar
[289] J., Davidson and P., Sibbertsen. Generating schemes for long memory processes: regimes, aggregation and linearity. Journal of Econometrics, 128(2):253–282, 2005. (Cited on page 224.)Google Scholar
[290] R. B., Davies and D. S., Harte. Tests for Hurst effect. Biometrika, 74(4):95–101, 1987. (Cited on page 112.)Google Scholar
[291] Yu. A., Davydov. The invariance principle for stationary processes. Theory of Probability and its Applications, 15:487–498, 1970. (Cited on page 111.)Google Scholar
[292] Ł., Dębowski. On processes with hyperbolically decaying autocorrelations. Journal of Time Series Analysis, 32:580–584, 2011. (Cited on page 571.)Google Scholar
[293] A., De Masi and P. A., Ferrari. Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process. Journal of Statistical Physics, 107(3-4):677–683, 2002. (Cited on page 168.)Google Scholar
[294] L., Decreusefond. Stochastic integration with respect to Volterra processes. Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 41(2):123–149, 2005. (Cited on page 435.)Google Scholar
[295] L., Decreusefond and D., Nualart. Hitting times for Gaussian processes. The Annals of Probability, 36(1):319–330, 2008. (Cited on page 436.)Google Scholar
[296] L., Decreusefond and A. S., Üstünel. Stochastic analysis of the fractional Brownian motion. Potential Analysis, 10:177–214, 1999. (Cited on pages 395 and 435.)Google Scholar
[297] H., Dehling, A., Rooch and M. S., Taqqu. Non-parametric change-point tests for long-range dependent data. Scandinavian Journal of Statistics. Theory and Applications, 40(1):153–173, 2013. (Cited on page 573.)Google Scholar
[298] P., Deift, A., Its and I., Krasovsky. Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities. Annals of Mathematics. Second Series, 174(2):1243–1299, 2011. (Cited on page 211.)Google Scholar
[299] M. A., Delgado and P. M., Robinson. Optimal spectral bandwidth for long memory. Statistica Sinica, 6(1):97–112, 1996. (Cited on pages 111, 565, and 572.)Google Scholar
[300] M. A., Delgado, J., Hidalgo and C., Velasco. Bootstrap assisted specification tests for the ARFIMA model. Econometric Theory, 27(5):1083–1116, 2011. (Cited on page 554.)Google Scholar
[301] A., Dembo, C. L., Mallows, and L. A., Shepp. Embedding nonnegative definite Toeplitz matrices in nonnegative definite circulant matrices, with applications to covariance estimation. IEEE Transactions on Information Theory, 35:1206–1212, 1989. (Cited on page 112.)Google Scholar
[302] R., Deo, M., Hsieh, C. M., Hurvich, and P., Soulier. Long memory in nonlinear processes. In Dependence in Probability and Statistics, volume 187 of Lecture Notes in Statist., pages 221–244. New York: Springer, 2006. (Cited on pages 573 and 611.)
[303] R. S., Deo and W. W., Chen. On the integral of the squared periodogram. Stochastic Processes and their Applications, 85(1):159–176, 2000. (Cited on page 554.)Google Scholar
[304] A., Deya, A., Neuenkirch and S., Tindel. A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 48(2):518–550, 2012. (Cited on page 436.)Google Scholar
[305] G., Didier and V., Pipiras. Gaussian stationary processes: adaptive wavelet decompositions, discrete approximations, and their convergence. The Journal of Fourier Analysis and Applications, 14(2):203–234, 2008. (Cited on page 465.)Google Scholar
[306] G., Didier and V., Pipiras. Adaptive wavelet decompositions of stationary time series. Journal of Time Series Analysis, 31(3):182–209, 2010. (Cited on page 465.)Google Scholar
[307] G., Didier and V., Pipiras. Integral representations and properties of operator fractional Brownian motions. Bernoulli, 17(1):1–33, 2011. (Cited on pages 479, 481, 484, and 536.)Google Scholar
[308] G., Didier and V., Pipiras. Exponents, symmetry groups and classification of operator fractional Brownian motions. Journal of Theoretical Probability, 25(2):353–395, 2012. (Cited on pages 494, 495, and 536.)Google Scholar
[309] G., Didier, M. M., Meerschaert, and V., Pipiras. The exponents of operator self-similar random fields. Journal of Mathematical Analysis and Applications, 448(2):1450–1466, 2017. (Cited on pages 509 and 538.)Google Scholar
[310] G., Didier, M. M., Meerschaert, and V., Pipiras. Domain and range symmetries of operator fractional Brownian fields. Preprint, 2016. (Cited on page 538.)
[311] F., Diebold and G., Rudebusch. Long memory and persistence in aggregate output. Journal of Monetary Economics, 24:189–209, 1989. (Cited on page 572.)Google Scholar
[312] F. X., Diebold and A., Inoue. Long memory and regime switching. Journal of Econometrics, 105(1):131–159, 2001. (Cited on pages 162, 222, and 225.)Google Scholar
[313] C. R., Dietrich and G. N., Newsam. A fast and exact simulation for multidimensional Gaussian stochastic simulations. Water Resources Research, 29(8):2861–2869, 1993. (Cited on page 112.)Google Scholar
[314] C. R., Dietrich and G. N., Newsam. Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix. SIAM Journal on Scientific Computing, 18(4):1088–1107, 1997. (Cited on page 112.)Google Scholar
[315] R. W., Dijkerman and R. R., Mazumdar. On the correlation structure of the wavelet coefficients of fractional Brownian motion. IEEE Trans. Inform. Theory, 40(5):1609–1612, 1994. (Cited on page 112.)Google Scholar
[316] Z., Ding, C. W. J., Granger, and R. F., Engle. A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1(1):83–106, 1993. (Cited on page 611.)Google Scholar
[317] G. S., Dissanayake, M. S., Peiris, and T., Proietti. State space modeling of Gegenbauer processes with long memory. Computational Statistics and Data Analysis, 2016. (Cited on page 110.)
[318] I., Dittmann and C. W. J., Granger. Properties of nonlinear transformations of fractionally integrated processes. Journal of Econometrics, 110(2):113–133, 2002. Long memory and nonlinear time series, Cardiff, 2000. (Cited on page 344.)Google Scholar
[319] R., Dmowska and B., Saltzman. Long-Range Persistence in Geophysical Time Series. Advances in Geophysics. Elsevier Science, 1999. (Cited on pages 111 and 610.)
[320] R. L., Dobrushin. Gaussian and their subordinated self-similar random generalized fields. The Annals of Probability, 7:1–28, 1979. (Cited on page 281.)Google Scholar
[321] R. L., Dobrushin and P., Major. Non-central limit theorems for nonlinear functionals of Gaussian fields. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 50(1):27–52, 1979. (Cited on pages 280, 343, 344, and 584.)Google Scholar
[322] C., Dombry and N., Guillotin-Plantard. A functional approach for random walks in random sceneries. Electronic Journal of Probability, 14:1495–1512, 2009. (Cited on pages 179 and 226.)Google Scholar
[323] C., Dombry and I., Kaj. The on-off network traffic model under intermediate scaling. Queueing Systems, 69(1):29–44, 2011. (Cited on page 224.)Google Scholar
[324] C., Dombry and I., Kaj. Moment measures of heavy-tailed renewal point processes: asymptotics and applications. ESAIM. Probability and Statistics, 17:567–591, 2013. (Cited on page 224.)Google Scholar
[325] J. L., Doob. Stochastic Processes. Wiley Classics Library. John Wiley & Sons Inc., New York, 1953. Reprint of the 1953 original, a Wiley-Interscience Publication. (Cited on page 476.)
[326] J. A., Doornik and M., Ooms. Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models. Computational Statistics & Data Analysis, 42(3):333–348, 2003. (Cited on pages 539 and 570.)Google Scholar
[327] R., Douc, E., Moulines and D. S., Stoffer. Nonlinear Time Series. Chapman & Hall/CRC Texts in Statistical Science Series. Chapman & Hall/CRC, Boca Raton, FL, 2014. Theory, methods, and applications with R examples. (Cited on page 14.)
[328] P., Doukhan, G., Oppenheim and M. S., Taqqu, editors. Theory and Applications of Long-Range Dependence. Boston: Birkhäuser, 2003. (Cited on page 610.)
[329] P., Driscoll. Smoothness of densities for area-like processes of fractional Brownian motion. Probability Theory and Related Fields, 155(1-2):1–34, 2013. (Cited on page 436.)Google Scholar
[330] R. M., Dudley and R., NorvaiŠa. Concrete Functional Calculus. Springer Monographs in Mathematics. New York: Springer, 2011. (Cited on page 435.)
[331] M., Dueker and R., Startz. Maximum-likelihood estimation of fractional cointegration with an application to US and Canadian bond rates. Review of Economics and Statistics, 80(3):420–426, 1998. (Cited on page 537.)Google Scholar
[332] N. G., Duffield and N., O'Connell. Large deviations and overflow probabilities for the general single-server queue, with applications. Mathematical Proceedings of the Cambridge Philosophical Society, 118(2):363–374, 1995. (Cited on page 611.)Google Scholar
[333] J. A., Duffy. A uniform law for convergence to the local times of linear fractional stable motions. The Annals of Applied Probability, 26(1):45–72, 2016. (Cited on page 111.)Google Scholar
[334] T. E., Duncan. Prediction for some processes related to a fractional Brownian motion. Statistics & Probability Letters, 76(2):128–134, 2006. (Cited on page 395.)Google Scholar
[335] T. E., Duncan. Mutual information for stochastic signals and fractional Brownian motion. IEEE Transactions on Information Theory, 54(10):4432–4438, 2008. (Cited on page 395.)Google Scholar
[336] T. E., Duncan and H., Fink. Corrigendum to “Prediction for some processes related to a fractional Brownian motion”. Statistics & Probability Letters, 81(8):1336–1337, 2011. (Cited on page 395.)Google Scholar
[337] T. E., Duncan, Y., Hu, and B., Pasik-Duncan. Stochastic calculus for fractional Brownian motion. I. Theory. SIAM Journal on Control and Optimization, 38(2):582–612, 2000. (Cited on page 435.)Google Scholar
[338] O., Durieu and Y., Wang. From infinite urn schemes to decompositions of self-similar Gaussian processes. Electronic Journal of Probability, 21, paper no. 43. (Cited on page 226.)
[339] D., Dürr, S., Goldstein, and J. L., Lebowitz. Asymptotics of particle trajectories in infinite one-dimensional systems with collisions. Communications on Pure and Applied Mathematics, 38(5):573–597, 1985. (Cited on pages 163, 165, and 225.)Google Scholar
[340] H., Dym and H. P., McKean. Fourier Series and Integrals. New York: Academic Press, 1972. (Cited on pages 575 and 577.)
[341] K., Dzhaparidze and H., van Zanten. A series expansion of fractional Brownian motion. Probability Theory and Related Fields, 130(1):39–55, 2004. (Cited on pages 463 and 465.)Google Scholar
[342] K., Dzhaparidze and H., van Zanten. Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion. The Annals of Probability, 33(2)620–644, 2005. (Cited on pages 455, 456, 459, 460, 461, 462, and 465.)Google Scholar
[343] K., Dzhaparidze and H., van Zanten. Optimality of an explicit series expansion of the fractional Brownian sheet. Statistics & Probability Letters, 71(4):295–301, 2005. (Cited on page 465.)Google Scholar
[344] K., Dzhaparidze, H., van Zanten, and P., Zareba. Representations of fractional Brownian motion using vibrating strings. Stochastic Processes and their Applications, 115(12):1928–1953, 2005. (Cited on page 465.)Google Scholar
[345] M., Eddahbi, R., Lacayo, J. L., Solé, J., Vives, and C. A., Tudor. Regularity of the local time for the d-dimensional fractional Brownian motion with N-parameters. Stochastic Analysis and Applications, 23(2):383–400, 2005. (Cited on page 432.)Google Scholar
[346] E., Eglói. Dilative Stability. PhD thesis, University of Debrecen, 2008. (Cited on page 110.)
[347] T., Ehrhardt and B., Silbermann. Toeplitz determinants with one Fisher-Hartwig singularity. Journal of Functional Analysis, 148(1):229–256, 1997. (Cited on page 211.)Google Scholar
[348] R. J., Elliott and J., van der Hoek. A general fractional white noise theory and applications to finance. Mathematical Finance. An International Journal of Mathematics, Statistics and Financial Economics, 13(2):301–330, 2003. (Cited on page 435.)Google Scholar
[349] C., Ellis and P., Wilson. Another look at the forecast performance of ARFIMA models. International Review of Financial Analysis, 13(1):63–81, 2004. (Cited on page 571.)Google Scholar
[350] P., Embrechts and M., Maejima. Selfsimilar Processes. Princeton Series in Applied Mathematics. Princeton University Press, 2002. (Cited on pages 44, 110, 536, and 610.)
[351] N., Enriquez. A simple construction of the fractional Brownian motion. Stochastic Processes and Their Applications, 109(2):203–223, 2004. (Cited on pages 222 and 224.)Google Scholar
[352] K., Falconer. Fractal Geometry. John Wiley & Sons, Ltd., Chichester, third edition, 2014. Mathematical Foundations and Applications. (Cited on page 612.)
[353] J., Fan and I., Gijbels. Local Polynomial Modelling and its Applications, volume 66 of Monographs on Statistics and Applied Probability. London: Chapman & Hall, 1996. (Cited on page 566.)Google Scholar
[354] V., Fasen. Modeling network traffic by a cluster Poisson input process with heavy and light-tailed file sizes. Queueing Systems, 66(4):313–350, 2010. (Cited on page 224.)Google Scholar
[355] G., Fay and A., Philippe. Goodness-of-fit test for long range dependent processes. European Series in Applied and Industrial Mathematics (ESAIM). Probability and Statistics, 6:239–258 (electronic), 2002. ISSN 1292-8100. New directions in time series analysis (Luminy, 2001). (Cited on page 554.)Google Scholar
[356] G., Faÿ, B., González-Arévalo, T., Mikosch, and G., Samorodnitsky. Modeling teletraffic arrivals by a Poisson cluster process. Queueing Systems, 54(2):121–140, 2006. (Cited on page 224.)Google Scholar
[357] G., Faÿ, E., Moulines, F., Roueff, and M. S., Taqqu. Estimators of long-memory: Fourier versus wavelets. Journal of Econometrics, 151(2):159–177, 2009. (Cited on page 112.)Google Scholar
[358] G., Faÿ, E., Moulines, F., Roueff, and M. S., Taqqu. Estimators of long-memory: Fourier versus wavelets. The Journal of Econometrics, 151(2):159–177, 2009. (Cited on page 574.)Google Scholar
[359] W., Feller. The asymptotic distribution of the range of sums of independent random variables. Annals of Mathematical Statistics, 22:427–432, 1951. (Cited on pages 87 and 111.)Google Scholar
[360] W., Feller. An Introduction to Probability Theory and its Applications. Vol. II. New York: John Wiley & Sons Inc., New York, 1966. (Cited on pages 92 and 561.)
[361] W., Feller. An Introduction to Probability Theory and its Applications. Vol. I, 3rd edition. New York: John Wiley & Sons Inc., New York, 1968. (Cited on pages 35 and 109.)
[362] Y., Feng and J., Beran. Filtered log-periodogram regression of long memory processes. Journal of Statistical Theory and Practice, 3(4):777–793, 2009. (Cited on page 111.)Google Scholar
[363] M., Ferrante and C., Rovira. Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H > ½. Bernoulli, 12(1):85–100, 2006. (Cited on page 436.)Google Scholar
[364] H., Fink, C., Klüppelberg, and M., Zähle. Conditional distributions of processes related to fractional Brownian motion. Journal of Applied Probability, 50(1):166–183, 2013. (Cited on page 395.)Google Scholar
[365] M. E., Fisher and R. E., Hartwig. Toeplitz determinants: some applications, theorems, and conjectures. In K. E., Shuler, editor, Advances in Chemical Physics: Stochastic Processes in Chemical Physics, volume 15, pages 333–353. Hoboken, NJ: John Wiley & Sons, Inc., 1968. (Cited on page 211.)
[366] P., Flandrin. Wavelet analysis and synthesis of fractional Brownian motion. IEEE Transactions on Information Theory, 38:910–917, 1992. (Cited on page 112.)Google Scholar
[367] P., Flandrin, P., Borgnat, and P.-O., Amblard. From stationarity to self-similarity, and back: Variations on the Lamperti transformation. In G., Rangarajan and M., Ding, editors, Processes with Long-Range Correlations, pages 88–117. Springer, 2003. (Cited on page 111.)
[368] R., Fox and M. S., Taqqu. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The Annals of Statistics, 14:517–532, 1986. (Cited on page 571.)Google Scholar
[369] R., Fox and M. S., Taqqu. Central limit theorems for quadratic forms in random variables having long-range dependence. Probability Theory and Related Fields, 74:213–240, 1987. (Cited on page 571.)Google Scholar
[370] B., Franke and T., Saigo. A self-similar process arising from a random walk with random environment in random scenery. Bernoulli, 16(3):825–857, 2010. (Cited on page 226.)Google Scholar
[371] P., Frederiksen and F. S., Nielsen. Testing for long memory in potentially nonstationary perturbed fractional processes. Journal of Financial Econometrics, page nbs027, 2013. (Cited on page 611.)Google Scholar
[372] P., Frederiksen and M. Ø., Nielsen. Bias-reduced estimation of long-memory stochastic volatility. Journal of Financial Econometrics, 6(4):496–512, 2008. (Cited on page 611.)Google Scholar
[373] P., Frederiksen, F. S., Nielsen, and M. Ø., Nielsen. Local polynomial Whittle estimation of perturbed fractional processes. Journal of Econometrics, 167(2):426–447, 2012. (Cited on page 611.)Google Scholar
[374] M. P., Frías, M. D., Ruiz-Medina, F. J., Alonso, and J. M., Angulo. Spatiotemporal generation of long-range dependence models and estimation. Environmetrics, 17(2):139–146, 2006. (Cited on page 538.)Google Scholar
[375] M. P., Frías, F. J., Alonso, M. D., Ruiz-Medina, and J. M., Angulo. Semiparametric estimation of spatial long-range dependence. Journal of Statistical Planning and Inference, 138(5):1479–1495, 2008. (Cited on page 537.)Google Scholar
[376] M. P., Frías, M. D., Ruiz-Medina, F. J., Alonso, and J. M., Angulo. Spectral-marginal-based estimation of spatiotemporal long-range dependence. Communications in Statistics. Theory and Methods, 38(1-2):103–114, 2009. (Cited on page 538.)Google Scholar
[377] Y., Fyodorov, B., Khoruzhenko and N., Simm. Fractional Brownian motion with Hurst index H = 0 and the Gaussian Unitary Ensemble. The Annals of Probability, 44(4):2980–3031, 2016. (Cited on page 110.)Google Scholar
[378] V. J., Gabriel and L. F., Martins. On the forecasting ability of ARFIMA models when infrequent breaks occur. The Econometrics Journal, 7(2):455–475, 2004. (Cited on page 573.)Google Scholar
[379] R., Gaigalas. A Poisson bridge between fractional Brownian motion and stable Lévy motion. Stochastic Processes and their Applications, 116(3):447–462, 2006. (Cited on page 145.)Google Scholar
[380] R., Gaigalas and I., Kaj. Convergence of scaled renewal processes and a packet arrival model. Bernoulli, 9(4):671–703, 2003. (Cited on pages 145 and 224.)Google Scholar
[381] F. R., Gantmacher. The Theory of Matrices. Vols. 1, 2. Translated by K. A., Hirsch. New York: Chelsea Publishing Co., 1959. (Cited on page 494.)
[382] M. J., Garrido-Atienza, P. E., Kloeden, and A., Neuenkirch. Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion. Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 60(2):151–172, 2009. (Cited on page 436.)Google Scholar
[383] D., Gasbarra, T., Sottinen and E., Valkeila. Gaussian bridges. In Stochastic analysis and applications, volume 2 of Abel Symp., pages 361–382. Berlin: Springer, 2007. (Cited on page 395.)
[384] D., Geman and J., Horowitz. Occupation densities. The Annals of Probability, 8(1):1–67, 1980. (Cited on pages 430, 433, and 436.)Google Scholar
[385] J. E., Gentle. Numerical Linear Algebra for Applications in Statistics. Statistics and Computing. New York: Springer-Verlag, 1998. (Cited on page 542.)
[386] M. G., Genton, O., Perrin and M. S., Taqqu. Self-similarity and Lamperti transformation for random fields. Stochastic Models, 23(3):397–411, 2007. (Cited on page 111.)Google Scholar
[387] J., Geweke and S., Porter-Hudak. The estimation and application of long memory time series models. Journal of Time Series Analysis, 4(4):221–238, 1983. (Cited on pages 89 and 111.)Google Scholar
[388] A. P., Ghosh, A., Roitershtein and A., Weerasinghe. Optimal control of a stochastic processing system driven by a fractional Brownian motion input. Advances in Applied Probability, 42(1):183–209, 2010. (Cited on page 436.)Google Scholar
[389] H., Gilsing and T., Sottinen. Power series expansions for fractional Brownian motions. Theory of Stochastic Processes, 9(3-4):38–49, 2003. (Cited on page 465.)Google Scholar
[390] M. S., Ginovian. On Toeplitz type quadratic functionals of stationary Gaussian processes. Probability Theory and Related Fields, 100(3):395–406, 1994. (Cited on page 571.)Google Scholar
[391] M. S., Ginovyan and A. A., Sahakyan. Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes. Probability Theory and Related Fields, 138(3-4):551–579, 2007. (Cited on page 571.)Google Scholar
[392] L., Giraitis. Central limit theorem for functionals of a linear process. Lithuanian Mathematical Journal, 25:25–35, 1985. (Cited on page 343.)Google Scholar
[393] L., Giraitis. Central limit theorem for polynomial forms I. Lithuanian Mathematical Journal, 29:109–128, 1989. (Cited on page 343.)Google Scholar
[394] L., Giraitis. Central limit theorem for polynomial forms II. Lithuanian Mathematical Journal, 29:338–350, 1989. (Cited on page 343.)Google Scholar
[395] L., Giraitis and P.M., Robinson. Edgeworth expansions for semiparametric Whittle estimation of long memory. The Annals of Statistics, 31(4):1325–1375, 2003. (Cited on page 572.)Google Scholar
[396] L., Giraitis and D., Surgailis. CLT and other limit theorems for functionals of Gaussian processes. Probability Theory and Related Fields, 70:191–212, 1985. (Cited on page 343.)Google Scholar
[397] L., Giraitis and D., Surgailis. Multivariate Appell polynomials and the central limit theorem. In E., Eberlein and M. S., Taqqu, editors, Dependence in Probability and Statistics, pages 21–71. New York: Birkhäuser, 1986. (Cited on page 343.)
[398] L., Giraitis and D., Surgailis. Limit theorem for polynomials of linear processes with long range dependence. Lietuvos Matematikos Rinkinys, 29:128–145, 1989. (Cited on page 343.)Google Scholar
[399] L., Giraitis and D., Surgailis. A central limit theorem for quadratic forms in strongly dependent linear variables and application to asymptotical normality of Whittle's estimate. Probability Theory and Related Fields, 86:87–104, 1990. (Cited on page 571.)Google Scholar
[400] L., Giraitis and D., Surgailis. Central limit theorem for the empirical process of a linear sequence with long memory. Journal of Statistical Planning and Inference, 80(1-2):81–93, 1999. (Cited on page 344.)Google Scholar
[401] L., Giraitis and M. S., Taqqu. Central limit theorems for quadratic forms with time-domain conditions. The Annals of Probability, 26:377–398, 1998. (Cited on page 571.)Google Scholar
[402] L., Giraitis and M., S. Taqqu. Whittle estimator for finite-variance non-Gaussian time series with long memory. The Annals of Statistics, 27(1):178–203, 1999. (Cited on page 571.)
[403] L., Giraitis, P. M., Robinson, and A., Samarov. Rate optimal semiparametric estimation of the memory parameter of the Gaussian time series with long range dependence1. Journal of Time Series Analysis, 18(1):49–60, 1997. (Cited on page 572.)Google Scholar
[404] L., Giraitis, P. M., Robinson, and A., Samarov. Adaptive semiparametric estimation of the long memory parameter. Journal of Multivariate Analysis, 72:183–207, 2000. (Cited on page 572.)Google Scholar
[405] L., Giraitis, P., Kokoszka, R., Leipus, and G., Teyssière. Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics, 112(2):265–294, 2003. (Cited on page 111.)Google Scholar
[406] L., Giraitis, H. L., Koul, and D., Surgailis. Large Sample Inference for Long Memory Processes. London: Imperial College Press, 2012. (Cited on pages 310, 311, 325, 539, 545, 546, 547, 549, 550, 571, 573, and 610.)
[407] R., Gisselquist. A continuum of collision process limit theorems. The Annals of Probability, 1:231–239, 1973. (Cited on pages 163 and 225.)Google Scholar
[408] A., Gloter and M., Hoffmann. Stochastic volatility and fractional Brownian motion. Stochastic Processes and their Applications, 113(1):143–172, 2004. (Cited on page 436.)Google Scholar
[409] B. V., Gnedenko and A. N., Kolmogorov. Limit distributions for sums of independent random variables. Readiing, MA: Addison-Wesley, 1954. (Cited on page 586.)
[410] A., Gnedin, B., Hansen and J., Pitman. Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws. Probability Surveys, 4:146–171, 2007. (Cited on page 228.)Google Scholar
[411] T., Gneiting. Power-law correlations, related models for long-range dependence and their simulation. Journal of Applied Probability, 37(4):1104–1109, 2000. (Cited on page 112.)Google Scholar
[412] T., Gneiting and M., Schlather. Stochastic models that separate fractal dimension and the Hurst effect. SIAM Review, 46(2):269–282 (electronic), 2004. (Cited on page 538.)Google Scholar
[413] T., Gneiting, H., Ševčíková, D. B., Percival, M., Schlather, and Y., Jiang. Fast and exact simulation of large Gaussian lattice systems in R2: Exploring the limits. Journal of Computational and Graphical Statistics, 15(3):483–501, 2006. (Cited on page 112.)Google Scholar
[414] F., Godet. Linear prediction of long-range dependent time series. ESAIM. Probability and Statistics, 13:115–134, 2009. ISSN 1292-8100. (Cited on page 571.)Google Scholar
[415] F., Godet. Prediction of long memory processes on same-realisation. Journal of Statistical Planning and Inference, 140(4):907–926, 2010. (Cited on page 571.)Google Scholar
[416] I., Gohberg, S., Goldberg and M. A., Kaashoek. Basic Classes of Linear Operators. Basel: Birkhäuser Verlag, 2003. (Cited on page 438.)
[417] E., Gonçalves and C., Gouriéroux. Agrégation de processus autorégressifs d'ordre 1. Annales d’Économie et de Statistique, 12:127–149, 1988. (Cited on page 223.)Google Scholar
[418] V. V., Gorodetskii. On convergence to semi-stable Gaussian processes. Theory of Probability and its Applications, 22:498–508, 1977. (Cited on page 111.)Google Scholar
[419] M., Gradinaru and I., Nourdin. Milstein's type schemes for fractional SDEs. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 45(4):1085–1098, 2009. (Cited on page 436.)Google Scholar
[420] M., Gradinaru, F., Russo and P., Vallois. Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H ≥ ¼. The Annals of Probability, 31(4):1772–1820, 2003. (Cited on page 435.)Google Scholar
[421] I. S., Gradshteyn and I. M., Ryzhik. Table of Integrals, Series, and Products, 7th edition. Amsterdam: Elsevier/Academic Press, 2007. Translated from the Russian, Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger, With one CD-ROM (Windows, Macintosh and UNIX). (Cited on pages 27, 30, 38, 50, 93, 98, 214, 295, 389, 489, 501, 533, and 550.)
[422] C. W. J., Granger. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, 14(2):227–238, 1980. (Cited on page 223.)Google Scholar
[423] C. W. J., Granger and N., Hyung. Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. Journal of Empirical Finance, 11(3):399–421, 2004. (Cited on page 225.)Google Scholar
[424] C. W. J., Granger and R., Joyeux. An introduction to long-memory time series and fractional differencing. Journal of Time Series Analysis, 1:15–30, 1980. (Cited on page 109.)Google Scholar
[425] T., Graves, R. B., Gramacy, C. L. E., Franzke, and N. W., Watkins. Efficient Bayesian inference for ARFIMA processes. Nonlinear Processes in Geophysics, 22:679–700, 2015. (Cited on page 573.)Google Scholar
[426] T., Graves, R. B., Gramacy, N. W., Watkins, and C. L., E. Franzke. A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA. Preprint, 2016. (Cited on page 109.)
[427] H. L., Gray, N.-F., Zhang, and W. A., Woodward. On generalized fractional processes. Journal of Time Series Analysis, 10(3):233–257, 1989. (Cited on page 110.)Google Scholar
[428] H. L., Gray, N.-F., Zhang, and W. A., Woodward. A correction: “On generalized fractional processes” [J. Time Ser. Anal. 10 (1989), no. 3, 233–257. Journal of Time Series Analysis, 15(5):561–562, 1994. (Cited on page 110.)Google Scholar
[429] U., Grenander. Abstract Inference. New York: John Wiley & Sons, 1981. (Cited on pages 384 and 385.)
[430] U., Grenander and G., Szegö. Toeplitz Forms and their Applications. California Monographs in Mathematical Sciences. Berkeley: University of California Press, 1958. (Cited on page 337.)
[431] M., Grigoriu. Simulation of stationary non-Gaussian translation processes. Journal of Engineering Mechanics, 124(2):121–126, 1998. (Cited on page 344.)Google Scholar
[432] G., Gripenberg. White and colored Gaussian noises as limits of sums of random dilations and translations of a single function. Electronic Communications in Probability, 16:507–516, 2011. (Cited on page 465.)Google Scholar
[433] G., Gripenberg and I., Norros. On the prediction of fractional Brownian motion. Journal of Applied Probability, 33:400–410, 1996. (Cited on page 395.)Google Scholar
[434] S. D., Grose, G. M., Martin, and D. S., Poskitt. Bias correction of persistence measures in fractionally integrated models. Journal of Time Series Analysis, 36(5):721–740, 2015. (Cited on page 574.)Google Scholar
[435] P., Guasoni. No arbitrage under transaction costs, with fractional Brownian motion and beyond. Mathematical Finance. An International Journal of Mathematics, Statistics and Financial Economics, 16(3):569–582, 2006. (Cited on page 435.)Google Scholar
[436] J. A., Gubner. Theorems and fallacies in the theory of long-range-dependent processes. IEEE Transactions on Information Theory, 51(3):1234–1239, 2005. (Cited on pages 27 and 106.)Google Scholar
[437] D., Guégan. How can we define the concept of long memory? An econometric survey. Econometric Reviews, 24(2):113–149, 2005. (Cited on page 109.)Google Scholar
[438] C. A., Guerin, H., Nyberg, O., Perrin, S., Resnick, H., Rootzén, and C., Stărică. Empirical testing of the infinite source Poisson data traffic model. Stochastic Models, 19:56–199, 2003. (Cited on pages 121 and 224.)Google Scholar
[439] P., Guggenberger and Y., Sun. Bias-reduced log-periodogram and Whittle estimation of the long-memory parameter without variance inflation. Econometric Theory, 22(5):863–912, 2006. ISSN 0266-4666. (Cited on pages 111, 572, and 573.)Google Scholar
[440] H., Guo, C. Y., Lim, and M. M., Meerschaert. Local Whittle estimator for anisotropic random fields. Journal of Multivariate Analysis, 100(5):993–1028, 2009. (Cited on pages 529 and 537.)Google Scholar
[441] A., Gupta and S., Joshi. Some studies on the structure of covariance matrix of discrete-time fBm. IEEE Transactions on Signal Processing, 56(10, part 1):4635–4650, 2008. (Cited on page 464.)Google Scholar
[442] A., Gut. Probability: A Graduate Course. Springer Texts in Statistics. New York: Springer, 2005. (Cited on pages 300, 314, and 317.)
[443] B., Haas and G., Miermont. Self-similar scaling limits of non-increasing Markov chains. Bernoulli, 17(4):1217–1247, 2011. (Cited on page 612.)Google Scholar
[444] M., Hairer. Ergodicity of stochastic differential equations driven by fractional Brownian motion. The Annals of Probability, 33(2):03–758, 2005. (Cited on page 436.)Google Scholar
[445] M., Hairer. Solving the KPZ equation. Annals of Mathematics. Second Series, 178(2):559–664, 2013. (Cited on page 227.)Google Scholar
[446] M., Hairer and N. S., Pillai. Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths. The Annals of Probability, 41(4):2544–2598, 2013. (Cited on page 436.)Google Scholar
[447] P., Hall, B.-Y., Jing, and S. N., Lahiri. On the sampling window method for long-range dependent data. Statistica Sinica, 8(4):1189–1204, 1998. (Cited on page 573.)Google Scholar
[448] K. H., Hamed. Improved finite-sample hurst exponent estimates using rescaled range analysis. Water Resources Research, 43(4), 2007. (Cited on page 111.)Google Scholar
[449] A., Hammond and S., Sheffield. Power law Pólya's urn and fractional Brownian motion. Probability Theory and Related Fields, 157(3-4):691–719, 2013. (Cited on pages 172, 173, 177, and 226.)Google Scholar
[450] E. J., Hannan. Multiple Time Series. John Wiley and Sons, Inc., 1970. (Cited on pages 470, 471, 478, and 479.)
[451] E. J., Hannan. The asymptotic theory of linear time series models. Journal of Applied Probability, 10:130–145, 1973. (Cited on page 570.)Google Scholar
[452] E. J., Hannan and B. G., Quinn. The determination of the order of an autoregression. Journal of the Royal Statistical Society. Series B. Methodological, 41(2):190–195, 1979. (Cited on page 552.)Google Scholar
[453] T., Hara. Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals. The Annals of Probability, 36(2):530–593, 2008. (Cited on page 227.)Google Scholar
[454] G. H., Hardy. Weierstrass's non-differentiable function. Transactions of the American Mathematical Society, 17:322–323, 1916. (Cited on page 216.)Google Scholar
[455] T. E., Harris. Diffusion with “collisions” between particles. Journal of Applied Probability, 2:323–338, 1965. (Cited on pages 163 and 225.)Google Scholar
[456] T. E., Harris. A correlation inequality for Markov processes in partially ordered state spaces. The Annals of Probability, 5(3):451–454, 1977. (Cited on page 172.)Google Scholar
[457] A. C., Harvey. 16 - long memory in stochastic volatility. In J., Knight and S., Satchell, editors, Forecasting Volatility in the Financial Markets (Third Edition), Quantitative Finance, pages 351–363. Oxford: Butterworth-Heinemann, 2007. (Cited on page 572.)
[458] J., Haslett and A. E., Raftery. Space-time modelling with long-memory dependence: assessing Ireland's wind power resource. Applied Statistics, 38:1–50, 1989. Includes discussion. (Cited on page 572.)Google Scholar
[459] U., Hassler and M., Olivares. Semiparametric inference and bandwidth choice under long memory: experimental evidence. İstatistik. Journal of the Turkish Statistical Association, 6(1):27–41, 2013. (Citedonpage 572.)Google Scholar
[460] U., Hassler, P. M. M., Rodrigues, and A., Rubia. Testing for general fractional integration in the time domain. Econometric Theory, 25(6):1793–1828, 2009. (Cited on page 574.)Google Scholar
[461] M. A., Hauser. Maximum likelihood estimators for ARMA and ARFIMA models: a Monte Carlo study. Journal of Statistical Planning and Inference, 80(1-2):229–255, 1999. (Cited on pages 550 and 571.)Google Scholar
[462] D., Heath, S., Resnick and G., Samorodnitsky. Heavy tails and long range dependence in on/off processes and associated fluid models. Mathematics of Operations Research, 23:146–165, 1998. (Cited on page 224.)Google Scholar
[463] H., Helgason, V., Pipiras and P., Abry. Fast and exact synthesis of stationary multivariate Gaussian time series using circulant embedding. Signal Processing, 91(5):1123–1133, 2011. (Cited on pages 112 and 470.)Google Scholar
[464] H., Helgason, V., Pipiras and P., Abry. Synthesis of multivariate stationary series with prescribed marginal distributions and covariance using circulant matrix embedding. Signal Processing, 91:1741–1758, 2011. (Cited on pages 339 and 344.)Google Scholar
[465] H., Helgason, V., Pipiras and P., Abry. Fast and exact synthesis of stationary multivariate Gaussian time series using circulant embedding. Signal Processing, 91(5):1123–1133, 2011. (Cited on page 486.)Google Scholar
[466] H., Helgason, V., Pipiras and P., Abry. Smoothing windows for the synthesis of Gaussian stationary random fields using circulant matrix embedding. Journal of Computational and Graphical Statistics, 23(3):616–635, 2014. (Cited on page 112.)Google Scholar
[467] P., Henrici. Applied and Computational Complex Analysis. New York: Wiley-Interscience [John Wiley & Sons], 1974. Volume 1: Power series—integration—conformal mapping—location of zeros, Pure and Applied Mathematics. (Cited on page 340.)
[468] M., Henry. Robust automatic bandwidth for long memory. Journal of Time Series Analysis, 22(3):293–316, 2001. (Cited on pages 565 and 572.)Google Scholar
[469] M., Henry. Bandwidth choice, optimal rates and adaptivity in semiparametric estimation of long memory. In Long Memory in Economics, pages 157–172. Berlin: Springer, 2007. (Cited on page 572.)
[470] M., Henry and P. M., Robinson. Bandwidth choice in Gaussian semiparametric estimation of long range dependence. In P. M., Robinson and M., Rosenblatt, editors, Athens Conference on Applied Probability and Time Series Analysis. Volume II: Time Series Analysis in Memory of E. J. Hannan, pages 220–232, New York: Springer-Verlag, 1996. Lecture Notes in Statistics, 115. (Cited on pages 565 and 572.)
[471] E., Herbin and E., Merzbach. Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion. Journal of Theoretical Probability, 22(4):1010–1029, 2009. (Cited on page 537.)Google Scholar
[472] C. C., Heyde. On modes of long-range dependence. Journal of Applied Probability, 39(4): 882–888, 2002. (Cited on page 109.)Google Scholar
[473] C. C., Heyde and R., Gay. Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence. Stochastic Processes and their Applications, 45:169–182, 1993. (Cited on page 571.)Google Scholar
[474] J., Hidalgo and Y., Yajima. Semiparametric estimation of the long-range parameter. Annals of the Institute of Statistical Mathematics, 55(4):705–736, 2003. (Cited on page 572.)Google Scholar
[475] N. J., Higham. Functions of Matrices. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2008. Theory and computation. (Cited on page 480.)
[476] H. C., Ho and T., Hsing. On the asymptotic expansion of the empirical process of long memory moving averages. The Annals of Statistics, 24:992–1024, 1996. (Cited on page 344.)Google Scholar
[477] H. C., Ho and T., Hsing. Limit theorems for functionals of moving averages. The Annals of Probability, 25:1636–1669, 1997. (Cited on pages 313, 315, and 344.)Google Scholar
[478] H. C., Ho and T. C., Sun. A central limit theorem for non-instantaneous filters of a stationary Gaussian process. Journal of Multivariate Analysis, 22:144–155, 1987. (Cited on pages 343 and 344.)Google Scholar
[479] N., Hohn, D., Veitch and P., Abry. Cluster processes: a natural language for network traffic. IEEE Transactions on Signal Processing, 51(8):2229–2244, 2003. (Cited on page 224.)Google Scholar
[480] S., Holan, T., McElroy, and So., Chakraborty. A Bayesian approach to estimating the long memory parameter. Bayesian Analysis, 4(1):159–190, 2009. (Cited on page 573.)Google Scholar
[481] R., Holley and D. W., Stroock. Central limit phenomena of various interacting systems. Annals of Mathematics. Second Series, 110(2):333–393, 1979. (Cited on page 226.)Google Scholar
[482] R., Horn and C., Johnson. Topics in Matrix Analysis. New York, NY: Cambridge University Press, 1991. (Cited on pages 467, 468, and 480.)
[483] L., Horváth and Q.-M., Shao. Limit theorems for quadratic forms with applications to Whittle's estimate. The Annals of Applied Probability, 9(1):146–187, 1999. (Cited on page 571.)Google Scholar
[484] J. R. M., Hosking. Fractional differencing. Biometrika, 68(1):165–176, 1981. (Cited on pages 43 and 109.)Google Scholar
[485] J. R. M., Hosking. Modeling persistence in hydrological time series using fractional differencing. Water Resources Research, 20:1898–1908, 1984. (Cited on pages 556 and 572.)Google Scholar
[486] J. R. M., Hosking. Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series. Journal of Econometrics, 73(1):261–284, 1996. (Cited on page 574.)Google Scholar
[487] Y., Hosoya. The quasi-likelihood approach to statistical inference on multiple time-series with long-range dependence. Journal of Econometrics, 73:217–236, 1996. (Cited on page 571.)Google Scholar
[488] C., Houdré and V., Pérez-Abreu, editors. Chaos expansions, multiple Wiener-Itô integrals and their applications. Probability and Stochastics Series. Boca Raton, FL: CRC Press, 1994. Papers from the workshop held in Guanajuato, July 27–31, 1992. (Cited on page 610.)
[489] C., Houdré and J., Villa. An example of infinite dimensional quasi-helix. In Stochastic models (Mexico City, 2002), volume 336 of Contemp. Math., pages 195–201. Providence, RI: Amer. Math. Soc., 2003. (Cited on pages 54, 55, and 110.)
[490] T., Hsing. Linear processes, long-range dependence and asymptotic expansions. Statistical Inference for Stochastic Processes, 3 (1-2): 19–29, 2000. 19th “Rencontres Franco-Belges de Statisticiens” (Marseille, 1998). (Cited on page 344.)Google Scholar
[491] Y., Hu. Integral transformations and anticipative calculus for fractional Brownian motions. Memoirs of the American Mathematical Society, 175(825), 2005. (Cited on page 436.)Google Scholar
[492] Y., Hu and B., Øksendal. Chaos expansion of local time of fractional Brownian motions. Stochastic Analysis and Applications, 20(4):815–837, 2002. (Cited on pages 432 and 436.)Google Scholar
[493] Y., Hu and B., Øksendal. Fractional white noise calculus and applications to finance. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 6(1):1–32, 2003. (Cited on page 435.)Google Scholar
[494] Y., Hu, J., Huang, D., Nualart and S., Tindel. Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency. Electronic Journal of Probability, 20:no. 55, 50 pp. (electronic), 2003. (Cited on page 227.)Google Scholar
[495] Y., Hu, Y., Liu and D., Nualart. Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions. The Annals of Applied Probability, 26(2):1147–1207, 2016. (Cited on pages 418, 419, and 424.)Google Scholar
[496] Y., Hu, D., Nualart, S., Tindel and F., Xu. Density convergence in the Breuer-Major theorem for Gaussian stationary sequences. Bernoulli, 21(4):2336–2350, 2015. (Cited on page 343.)Google Scholar
[497] J., Hualde and P. M., Robinson. Semiparametric inference in multivariate fractionally cointegrated systems. Journal of Econometrics, 157(2):492–511, 2010. (Cited on page 537.)Google Scholar
[498] J., Hualde and P. M., Robinson. Gaussian pseudo-maximum likelihood estimation of fractional time series models. The Annals of Statistics, 39(6):3152–3181, 2011. (Cited on page 551.)Google Scholar
[499] W. N., Hudson and J. D., Mason. Operator-self-similar processes in a finite-dimensional space. Transactions of the American Mathematical Society, 273(1):281–297, 1982. (Cited on pages 493 and 536.)Google Scholar
[500] Y., Huh, J.S., Kim, S. H., Kim, and M.W., Suh. Characterizing yarn thickness variation by correlograms. Fibers and Polymers, 6(1):66–71, 2005. (Cited on page 225.)Google Scholar
[501] H. E., Hurst. Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116:770–779, 1951. (Cited on pages 84, 108, and 111.)Google Scholar
[502] C. M., Hurvich. Model selection for broadband semiparametric estimation of long memory in time series. Journal of Time Series Analysis, 22(6):679–709, 2001. (Cited on page 573.)Google Scholar
[503] C. M., Hurvich. Multistep forecasting of long memory series using fractional exponential models. International Journal of Forecasting, 18(2):167–179, 2002. (Cited on page 571.)Google Scholar
[504] C. M., Hurvich and K. I., Beltrao. Automatic semiparametric estimation of the memory parameter of a long-memory time series. Journal of Time Series Analysis, 15:285–302, 1994. (Cited on page 573.)Google Scholar
[505] C. M., Hurvich and J., Brodsky. Broadband semiparametric estimation of the memory parameter of a long-memory time series using fractional exponential models. Journal of Time Series Analysis, 22(2):221–249, 2001. (Cited on page 573.)Google Scholar
[506] C. M., Hurvich and W. W., Chen. An efficient taper for potentially overdifferenced long-memory time series. Journal of Time Series Analysis, 21(2):155–180, 2000. (Cited on page 566.)Google Scholar
[507] C. M., Hurvich and R. S., Deo. Plug-in selection of the number of frequencies in regression estimates of the memory parameter of a long-memory time series. Journal of Time Series Analysis, 20:331–341, 1999. (Cited on pages 111 and 573.)Google Scholar
[508] C. M., Hurvich and B. K., Ray. Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. Journal of Time Series Analysis, 16(1):17–41, 1995. (Cited on page 573.)Google Scholar
[509] C. M., Hurvich and B. K., Ray. The local Whittle estimator of long-memory stochastic volatility. Journal of Financial Econometrics, 1(3):445–470, 2003. (Cited on page 611.)Google Scholar
[510] C. M., Hurvich, R., Deo and J., Brodsky. The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long-memory time series. Journal of Time Series Analysis, 19:19–46, 1998. (Cited on pages 111 and 573.)Google Scholar
[511] C. M., Hurvich, E., Moulines and P., Soulier. The FEXP estimator for potentially non-stationary linear time series. Stochastic Processes and their Applications, 97(2):307–340, 2002. (Cited on page 573.)Google Scholar
[512] C. M., Hurvich, E., Moulines and P., Soulier. Estimating long memory in volatility. Econometrica, 73(4):1283–1328, 2005. (Cited on page 611.)Google Scholar
[513] F., Iacone. Local Whittle estimation of the memory parameter in presence of deterministic components. Journal of Time Series Analysis, 31(1):37–49, 2010. (Cited on pages 225 and 573.)Google Scholar
[514] I. A., Ibragimov. An estimate for the spectral function of a stationary Gaussian process. Teor. Verojatnost. i Primenen, 8:391–430, 1963. (Cited on page 343.)Google Scholar
[515] I. A., Ibragimov and Yu. V., Linnik. Independent and Stationary Sequences of Random Variables. The Netherlands: Wolters-Nordhoff, 1971. (Cited on pages 583 and 586.)
[516] SAS Institute Inc. SAS/IML 9.2 Users Guide. Cary, NC: SAS Institute Inc., 2008. (Cited on page 572.)
[517] C.-K., Ing, H.-T., Chiou, and M., Guo. Estimation of inverse autocovariance matrices for long memory processes. Bernoulli, 22(3):1301–1330, 2016. (Cited on page 574.)Google Scholar
[518] A., Inoue. Abel-Tauber theorems for Fourier-Stieltjes coefficients. Journal of Mathematical Analysis and Applications, 211(2):460–480, 1997. (Cited on page 109.)Google Scholar
[519] A., Inoue. Asymptotic behavior for partial autocorrelation functions of fractional ARIMA processes. The Annals of Applied Probability, 12(4):1471–1491, 2002. (Cited on page 555.)Google Scholar
[520] A., Inoue. AR and MA representation of partial autocorrelation functions, with applications. Probability Theory and Related Fields, 140(3-4):523–551, 2008. (Cited on page 109.)Google Scholar
[521] A., Inoue and Y., Kasahara. Explicit representation of finite predictor coefficients and its applications. The Annals of Statistics, 34(2):973–993, 2006. (Cited on page 571.)Google Scholar
[522] A., Inoue, Y., Nakano and V., Anh. Linear filtering of systems with memory and application to finance. Journal of Applied Mathematics and Stochastic Analysis. JAMSA, pages Art. ID 53104, 26, 2006. (Cited on page 395.)
[523] A., Iouditsky, E., Moulines and P., Soulier. Adaptive estimation of the fractional differencing coefficient. Bernoulli, 7(5):699–731, 2001. (Cited on page 573.)Google Scholar
[524] K., Itô. Multiple Wiener integral. Journal of the Mathematical Society of Japan, 3:157–169, 1951. (Cited on page 280.)Google Scholar
[525] A. V., Ivanov and N. N., Leonenko. Statistical Analysis of Random Fields.Dordrecht/Boston/London: Kluwer Academic Publishers, 1989. Translated from the Russian, 1986 edition. (Cited on page 344.)
[526] A., Jach and P., Kokoszka. Wavelet-domain test for long-range dependence in the presence of a trend. Statistics. A Journal of Theoretical and Applied Statistics, 42(2):101–113, 2008. (Cited on page 225.)Google Scholar
[527] S., Jaffard, B., Lashermes and P., Abry. Wavelet leaders in multifractal analysis. In Wavelet analysis and applications, Appl. Numer. Harmon. Anal., pages 201–246. Basel: Birkhäuser, 2007. (Cited on page 612.)
[528] S., Jaffard, C., Melot, R., Leonarduzzi, H., Wendt, P., Abry, S. G., Roux, and M. E., Torres. p-exponent and p-leaders, part i: Negative pointwise regularity. Physica A: Statistical Mechanics and its Applications, 448:300–318, 2016. (Cited on page 612.)Google Scholar
[529] S., Janson. Gaussian Hilbert Spaces, volume 129 of Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press, 1997. (Cited on pages 276, 281, and 610.)
[530] M. D., Jara. Nonequilibrium scaling limit for a tagged particle in the simple exclusion process with long jumps. Communications on Pure and Applied Mathematics, 62(2):198–214, 2009. (Cited on page 226.)Google Scholar
[531] M. D., Jara and T., Komorowski. Limit theorems for some continuous-time random walks. Advances in Applied Probability, 43(3):782–813, 2011. (Cited on page 228.)Google Scholar
[532] M. D., Jara and C., Landim. Nonequilibrium central limit theorem for a tagged particle in symmetric simple exclusion. Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 42(5):567–577, 2006. (Cited on page 226.)Google Scholar
[533] M. D., Jara, C., Landim and S., Sethuraman. Nonequilibrium fluctuations for a tagged particle in mean-zero one-dimensional zero-range processes. Probability Theory and Related Fields, 145(3-4):565–590, 2009. (Cited on page 226.)Google Scholar
[534] S., Johansen and M. Ø., Nielsen. Likelihood inference for a nonstationary fractional autoregressive model. Journal of Econometrics, 158(1):51–66, 2010. (Cited on page 537.)Google Scholar
[535] S., Johansen and M. Ø., Nielsen. Likelihood inference for a fractionally cointegrated vector autoregressive model. Econometrica, 80(6):2667–2732, 2012. (Cited on page 537.)Google Scholar
[536] M., Jolis and N., Viles. Continuity in the Hurst parameter of the law of the Wiener integral with respect to the fractional Brownian motion. Statistics & Probability Letters, 80(7-8):566–572, 2010. (Cited on page 395.)Google Scholar
[537] C., Jost. On the connection between Molchan-Golosov and Mandelbrot-Van Ness representations of fractional Brownian motion. Journal of Integral Equations and Applications, 20(1):93–119, 2008. (Citedonpage 395.)Google Scholar
[538] G., Jumarie. Stochastic differential equations with fractional Brownian motion input. International Journal of Systems Science, 24(6):1113–1131, 1993. (Cited on page 435.)Google Scholar
[539] P., Jung and G., Markowsky. Random walks at random times: convergence to iterated Lévy motion, fractional stable motions, and other self-similar processes. The Annals of Probability, 41(4):2682–2708, 2013. (Cited on page 226.)Google Scholar
[540] P., Jung and G., Markowsky. Hölder continuity and occupation-time formulas for fBm self-intersection local time and its derivative. Journal of Theoretical Probability, 28(1):299–312, 2015. (Citedonpage 436.)Google Scholar
[541] P., Jung, T., Owada and G., Samorodnitsky. Functional central limit theorem for negatively dependent heavy-tailed stationary infinitely divisible processes generated by conservative flows. Preprint, 2015. (Cited on page 228.)
[542] Z. J., Jurek and J. D., Mason. Operator-Limit Distributions in Probability Theory. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. New York: John Wiley & Sons Inc., 1993. A Wiley-Interscience Publication. (Cited on pages 494 and 535.)
[543] T., Kaarakka and P., Salminen. On fractional Ornstein-Uhlenbeck processes. Communications on Stochastic Analysis, 5(1):121–133, 2011. (Cited on page 395.)Google Scholar
[544] J.-P., Kahane and J., Peyrière. Sur certaines martingales de Benoit Mandelbrot. Advances in Mathematics, 22(2):131–145, 1976. (Cited on page 612.)Google Scholar
[545] I., Kaj. Stochastic Modeling in Broadband Communications Systems. SIAM Monographs on Mathematical Modeling and Computation. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2002. (Cited on page 224.)
[546] I., Kaj and M. S., Taqqu. Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach. In In and out of equilibrium. 2, volume 60 of Progr. Probab., pages 383–427. Basel: Birkhäuser, 2008. (Cited on pages 149 and 224.)
[547] I., Kaj, L., Leskelä, I., Norros, and V., Schmidt. Scaling limits for random fields with long-range dependence. The Annals of Probability, 35(2):528–550, 2007. (Cited on page 224.)Google Scholar
[548] A., Kamont. On the fractional anisotropic Wiener field. Probability and Mathematical Statistics, 16(1):85–98, 1996. (Cited on page 537.)Google Scholar
[549] I., Karatzas and S. E., Shreve. Brownian Motion and Stochastic Calculus, 2nd edition, volume 113 of Graduate Texts in Mathematics. New York: Springer-Verlag, 1991. (Cited on pages 14 and 452.)
[550] S., Kechagias and V., Pipiras. Identification, estimation and applications of a bivariate long-range dependent time series model with general phase. Preprint, 2015. (Cited on pages 502 and 536.)
[551] S., Kechagias and V., Pipiras. Definitions and representations of multivariate long-range dependent time series. Journal of Time Series Analysis, 36(1):1–25, 2015. (Cited on pages 470, 502, 535, and 536.)Google Scholar
[552] M., Kendall and A., Stuart. The Advanced Theory of Statistics. Vol. 1, 4th edition. New York: Macmillan Publishing Co., Inc., 1977. Distribution Theory. (Cited on page 332.)
[553] H., Kesten and F., Spitzer. A limit theorem related to a new class of self-similar processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 50:5–25, 1979. (Cited on pages 177 and 226.)Google Scholar
[554] H., Kesten, M. V., Kozlov, and F., Spitzer. A limit law for random walk in a random environment. Compositio Mathematica, 30:145–168, 1975. (Cited on page 178.)Google Scholar
[555] C. S., Kim and P. C., Phillips. Log periodogram regression: the nonstationary case, 2006. Cowles Foundation Discussion Paper. (Cited on page 111.)
[556] Y. M., Kim and D. J., Nordman. Properties of a block bootstrap under long-range dependence. Sankhya A. Mathematical Statistics and Probability, 73(1):79–109, 2011. (Cited on page 574.)Google Scholar
[557] Y. M., Kim and D. J., Nordman. A frequency domain bootstrap for Whittle estimation under long-range dependence. J. Multivariate Anal., 115:405–420, 2013. (Cited on page 574.)Google Scholar
[558] J. F. C., Kingman. Poisson Processes, volume 3 of Oxford Studies in Probability. New York:The Clarendon Press Oxford University Press, 1993. Oxford Science Publications. (Cited on pages 125, 127, 593, and 594.)
[559] C., Kipnis. Central limit theorems for infinite series of queues and applications to simple exclusion. The Annals of Probability, 14(2):397–408, 1986. (Cited on page 226.)Google Scholar
[560] C., Kipnis and S. R. S., Varadhan. Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Communications in Mathematical Physics, 104(1):1–19, 1986. (Cited on page 226.)Google Scholar
[561] J., Klafler and I. M., Sokolov. Anomalous diffusion spreads its wings. Physics World, 18 (8): 29–32, 2005. (Cited on page 227.)Google Scholar
[562] F. C., Klebaner. Introduction to Stochastic Calculus with Applications, 2nd edition. London: Imperial College Press, 2005. (Cited on page 382.)
[563] V, KlemeŠ. The Hurst pheomenon: a puzzle? Water Resources Research, 10(4):675–688, 1974. (Cited on pages 111 and 225.)Google Scholar
[564] M. L., Kleptsyna and A., Le Breton. Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises. Statistical Inference for Stochastic Processes, 5(3):249–271, 2002. (Cited on page 395.)Google Scholar
[565] M. L., Kleptsyna, P. E., Kloeden, and V. V., Anh. Linear filtering with fractional Brownian motion. Stochastic Analysis and Applications, 16(5):907–914, 1998. (Cited on page 395.)Google Scholar
[566] M. L., Kleptsyna, A., Le Breton, and M.-C., Roubaud. Parameter estimation and optimal filtering for fractional type stochastic systems. Statistical Inference for Stochastic Processes, 3(1-2):173–182, 2000. 19th “Rencontres Franco-Belges de Statisticiens” (Marseille, 1998). (Cited on page 395.)Google Scholar
[567] F., Klingenhöfer and M., Zähle. Ordinary differential equations with fractal noise. Proceedings of the American Mathematical Society, 127(4):1021–1028, 1999. (Cited on page 414.)Google Scholar
[568] C., Klüppelberg and C., Kühn. Fractional Brownian motion as a weak limit of Poisson shot noise processes—with applications to finance. Stochastic Processes and their Applications, 113(2):333–351, 2004. (Cited on page 225.)Google Scholar
[569] C., Klüppelberg and T., Mikosch. Explosive Poisson shot noise processes with applications to risk reserves. Bernoulli, 1(1-2):125–147, 1995. (Cited on page 225.)Google Scholar
[570] C., Klüppelberg, T., Mikosch, and A., Schärf. Regular variation in the mean and stable limits for poisson shot noise. Bernoulli, 9(3):467–496, 2003. (Cited on page 225.)Google Scholar
[571] P. S., Kokoszka and M. S., Taqqu. Fractional ARIMA with stable innovations. Stochastic Processes and their Applications, 60:19–47, 1995. (Cited on pages 82, 83, 107, 111, and 573.)Google Scholar
[572] P. S., Kokoszka and M. S., Taqqu. Infinite variance stable moving averages with long memory. Journal of Econometrics, 73:79–99, 1996. (Cited on pages 82 and 111.)Google Scholar
[573] P. S., Kokoszka and M. S., Taqqu. Parameter estimation for infinite variance fractional ARIMA. The Annals of Statistics, 24:1880–1913, 1996. (Cited on pages 82, 111, and 573.)Google Scholar
[574] P. S., Kokoszka and M. S., Taqqu. Can one use the Durbin-Levinson algorithm to generate infinite variance fractional ARIMA time series. Journal of Time Series Analysis, 22(3):317–337, 2001. (Citedonpage 107.)Google Scholar
[575] A. N., Kolmogorov. Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS (N.S.), 26:115–118, 1940. (Cited on page 110.)Google Scholar
[576] T., Konstantopoulos and S.-J., Lin. Macroscopic models for long-range dependent network traffic. Queueing Systems, 28:215–243, 1998. (Cited on page 224.)Google Scholar
[577] S., Kotz, N., Balakrishnan and N. L., Johnson. Continuous Multivariate Distributions. Vol. 1, 2nd edition. New York: Wiley Series in Probability and Statistics: Applied Probability and Statistics. Wiley-Interscience, 2000. Models and applications. (Cited on page 332.)
[578] D., Koutsoyiannis. Uncertainty, entropy, scaling and hydrological statistics. 1. Marginal distributional properties of hydrological processes and state scaling/Incertitude, entropie, effet d’échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d’état. Hydrological Sciences Journal, 50(3):381–404, 2005. (Cited on page 228.)Google Scholar
[579] L., Kristoufek. Testing power-law cross-correlations: rescaled covariance test. The European Physical Journal B. Condensed Matter and Complex Systems, 86(10):86:418, 11, 2013. (Cited on page 537.)Google Scholar
[580] K., Kubilius and V., Skorniakov. On some estimators of the Hurst index of the solution of SDE driven by a fractional Brownian motion. Statistics & Probability Letters, 109:159–167, 2016. (Citedonpage 436.)Google Scholar
[581] R., Kulik and P., Soulier. Limit theorems for long-memory stochastic volatility models with infinite variance: partial sums and sample covariances. Advances in Applied Probability, 44(4):1113–1141, 2012. (Cited on page 111.)Google Scholar
[582] H., Künsch. Statistical aspects of self-similar processes. Proceedings of the First World Congress of the Bernoulli Society, 1:67–74, 1987. (Cited on page 572.)Google Scholar
[583] M., Kunze. An Introduction to Malliavin Calculus. Lecture Notes, 2013. (Cited on page 603.)
[584] M., Kuronen and L., Leskelä. Hard-core thinnings of germ-grain models with power-law grain sizes. Advances in Applied Probability, 45(3):595–625, 2013. (Cited on page 224.)Google Scholar
[585] T. G., Kurtz. Limit theorems for workload input models. In F. P., Kelly, S., Zachary, and I., Ziedins, editors, Stochastic Networks: Theory and Applications, pages 339–366. Oxford: Clarendon Press, 1996. (Cited on page 224.)
[586] S., Kwapień and N. A., Woyczyński. Random Series and Stochastic Integrals: Single and multiple. Boston: Birkhäuser, 1992. (Cited on page 463.)
[587] R. G., Laha and V. K., Rohatgi. Operator self-similar stochastic processes in Rd. Stochastic Processes and their Applications, 12(1):73–84, 1982. (Cited on page 536.)Google Scholar
[588] S. N., Lahiri and P. M., Robinson. Central limit theorems for long range dependent spatial linear processes. Bernoulli, 22(1):345–375, 2016. (Cited on page 344.)Google Scholar
[589] J., Lamperti. Semi-stable stochastic processes. Transactions of the American Mathematical Society, 104:62–78, 1962. (Cited on pages 66, 68, 69, 110, and 111.)Google Scholar
[590] J., Lamperti. Semi-stable Markov processes. I. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 22:205–225, 1972. (Cited on page 612.)Google Scholar
[591] J. A., Lane. The central limit theorem for the Poisson shot-noise process. Journal of Applied Probability, 21(2):287–301, 1984. (Cited on page 225.)
[592] K., Lange. Optimization. Springer Texts in Statistics. New York: Springer-Verlag, 2004. (Cited on page 540.)
[593] N., Lanjri Zadi and D., Nualart. Smoothness of the law of the supremum of the fractional Brownian motion. Electronic Communications in Probability, 8:102–111 (electronic), 2003. (Cited on pages 434 and 436.)Google Scholar
[594] K., Łasak and C., Velasco. Fractional cointegration rank estimation. Journal of Business & Economic Statistics, 33(2):241–254, 2015. (Cited on page 537.)Google Scholar
[595] F., Lavancier. Long memory random fields. In Dependence in Probability and Statistics, volume 187 of Lecture Notes in Statist., pages 195–220. New York: Springer, 2006. (Cited on pages 524, 529, and 537.)
[596] F., Lavancier. Invariance principles for non-isotropic long memory random fields. Statistical Inference for Stochastic Processes, 10(3):255–282, 2007. (Cited on pages 529 and 537.)Google Scholar
[597] F., Lavancier, A., Philippe and D., Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 79(23):2415–2421, 2009. (Cited on pages 491 and 536.)Google Scholar
[598] G. F., Lawler. Conformally Invariant Processes in the Plane, volume 114 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society, 2005. (Cited on page 227.)
[599] A. J., Lawrence and N. T., Kottegoda. Stochastic modelling of riverflow time series. Journal of the Royal Statistical Society, A 140(1):1–47, 1977. (Cited on page 111.)Google Scholar
[600] A., Le Breton. Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion. Statistics & Probability Letters, 38(3):263–274, 1998. (Cited on page 395.)
[601] N. N., Lebedev. Special Functions and their Applications. Dover Publications Inc., New York, 1972. Revised edition, translated from the Russian and edited by Richard A. Silverman, Unabridged and corrected republication. (Cited on pages 266, 280, and 363.)
[602] J., Lebovits and J. L., Véhel. White noise-based stochastic calculus with respect to multifractional Brownian motion. Stochastics, 86(1):87–124, 2014. (Cited on page 611.)Google Scholar
[603] P., Lei and D., Nualart. A decomposition of the bifractional Brownian motion and some applications. Statistics & Probability Letters, 79(5):619–624, 2009. (Cited on pages 55, 56, and 110.)Google Scholar
[604] R., Leipus and D., Surgailis. Random coefficient autoregression, regime switching and long memory. Advances in Applied Probability, 35(3):737–754, 2003. (Cited on page 223.)Google Scholar
[605] R., Leipus, G., Oppenheim, A., Philippe, and M.-C., Viano. Orthogonal series density estimation in a disaggregation scheme. Journal of Statistical Planning and Inference, 136(8):2547–2571, 2006. (Cited on page 223.)Google Scholar
[606] R., Leipus, A., Philippe, D., Puplinskaitė, and D., Surgailis. Aggregation and long memory: recent developments. Journal of the Indian Statistical Association, 52(1):81–111, 2014. (Cited on page 224.)Google Scholar
[607] W. E., Leland, M. S., Taqqu, W., Willinger, and D. V., Wilson. On the self-similar nature of Ethernet traffic (Extended version). IEEE/ACM Transactions on Networking, 2:1–15, 1994. (Cited on page 224.)Google Scholar
[608] J. A., León and S., Tindel. Malliavin calculus for fractional delay equations. Journal of Theoretical Probability, 25(3):854–889, 2012. (Cited on page 436.)Google Scholar
[609] R., Leonarduzzi, H., Wendt, P., Abry, S., Jaffard, C., Melot, S. G., Roux, and M. E., Torres. p-exponent and p-leaders, part ii: Multifractal analysis. Relations to detrended fluctuation analysis. Physica A: Statistical Mechanics and its Applications, 448:319–339, 2016. (Cited on page 612.)Google Scholar
[610] N., Leonenko and A., Olenko. Tauberian and Abelian theorems for long-range dependent random fields. Methodology and Computing in Applied Probability, 15(4):715–742, 2013. (Cited on pages 526, 529, and 537.)Google Scholar
[611] N., Leonenko and E., Taufer. Convergence of integrated superpositions of Ornstein-Uhlenbeck processes to fractional Brownian motion. Stochastics. An International Journal of Probability and Stochastic Processes, 77(6):477–499, 2005. (Cited on page 224.)Google Scholar
[612] N. N., Leonenko. Limit Theorems for Random Fields with Singular Spectrum. Kluwer, 1999. (Cited on pages 344, 537, and 610.)
[613] N. N., Leonenko and A. Ya., Olenko. Tauberian theorems for correlation functions and limit theorems for spherical averages of random fields. Random Operators and Stochastic Equations, 1(1):58–68, 1992. (Cited on page 344.)Google Scholar
[614] N. N., Leonenko and V. N., Parkhomenko1. Central limit theorem for non-linear transforms of vector Gaussian fields. Ukrainian Mathematical Journal, 42(8):1057–1063, 1990. (Cited on page 344.)Google Scholar
[615] N. N., Leonenko, M. D., Ruiz-Medina, and M. S., Taqqu. Non-central limit theorems for random fields subordinated to gamma-correlated random fields. To appear in Bernoulli, 2017. (Cited on page 343.)
[616] N. N., Leonenko, M. D., Ruiz-Medina, and M. S., Taqqu. Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence. Stochastic Analysis and Applications, 35(1):144–177, 2017. (Cited on page 343.)Google Scholar
[617] J. B., Levy and M. S., Taqqu. Renewal reward processes with heavy-tailed interrenewal times and heavy-tailed rewards. Bernoulli, 6(1):23–44, 2000. (Cited on page 224.)Google Scholar
[618] C., Lévy-Leduc and M. S., Taqqu. Long-range dependence and the rank of decompositions. In D., Carfi, M.L., Lapidus, E.P.J., Pearse, and M., van Frankenhuijsen, editors, Fractal geometry and dynamical systems in pure and applied mathematics. II. Fractals in applied mathematics, volume 601 of Contemp. Math., pages 289–305. American Mathematical Society, 2013. (Cited on pages 343 and 344.)
[619] C., Lévy-Leduc, H., Boistard, E., Moulines, M. S., Taqqu, and V. A., Reisen. Large sample behaviour of some well-known robust estimators under long-range dependence. Statistics. A Journal of Theoretical and Applied Statistics, 45(1):59–71, 2011. (Cited on page 573.)Google Scholar
[620] C., Lévy-Leduc, H., Boistard, E., Moulines, M. S., Taqqu, and V. A., Reisen. Robust estimation of the scale and of the autocovariance function of Gaussian short- and long-range dependent processes. Journal of Time Series Analysis, 32(2):135–156, 2011. (Cited on page 574.)Google Scholar
[621] A., Lewbel. Aggregation and simple dynamics. The American Economic Review, 84(4):905–918, 1994. (Cited on page 224.)Google Scholar
[622] L., Li. Response to comments on “PCA based Hurst exponent estimator for fBm signals under disturbances”. ArXiv preprint arXiv:0805.3002, 2010. (Cited on page 464.)
[623] L., Li, J., Hu, Y., Chen and Y., Zhang. PCA based Hurst exponent estimator for fBm signals under disturbances. IEEE Transactions on Signal Processing, 57(7):2840–2846, 2009. (Cited on page 464.)Google Scholar
[624] W., Li, C., Yu, A., Carriquiry and W., Kliemann. The asymptotic behavior of the R/S statistic for fractional Brownian motion. Statistics & Probability Letters, 81(1):83–91, 2011. (Cited on page 111.)Google Scholar
[625] Y., Li and Y., Xiao. Multivariate operator-self-similar random fields. Stochastic Processes and their Applications, 121(6):1178–1200, 2011. (Cited on page 538.)Google Scholar
[626] Y., Li, W., Wang and Y., Xiao. Exact moduli of continuity for operator-scaling Gaussian random fields. Bernoulli, 21(2):930–956, 2015. (Cited on page 537.)Google Scholar
[627] O., Lieberman and P., C. B., Phillips. Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter. Econometric Theory, 20(3):464–484, 2004. (Cited on pages 571 and 572.)Google Scholar
[628] O., Lieberman and P. C. B., Phillips. Expansions for approximate maximum likelihood estimators of the fractional difference parameter. The Econometrics Journal, 8(3):367–379, 2005. (Cited on page 572.)Google Scholar
[629] O., Lieberman and P. C. B., Phillips. Refined inference on long memory in realized volatility. Econometric Reviews, 27(1-3) 254–267, 2008. (Cited on page 611.)Google Scholar
[630] O., Lieberman, J., Rousseau and D. M., Zucker. Small-sample likelihood-based inference in the ARFIMA model. Econometric Theory, 16(2):231–248, 2000. (Cited on page 571.)Google Scholar
[631] O., Lieberman, R., Rosemarin and J., Rousseau. Asymptotic theory for maximum likelihood estimation of the memory parameter in stationary Gaussian processes. Econometric Theory, 28(2):457–470, 2012. (Cited on pages 540, 546, and 571.)Google Scholar
[632] T. M., Liggett. Interacting Particle Systems. Classics in Mathematics. Berlin: Springer-Verlag, 2005. Reprint of the 1985 original. (Cited on pages 168 and 226.)
[633] C. Y., Lim, M. M., Meerschaert, and H.-P., Scheffler. Parameter estimation for operator scaling random fields. Journal of Multivariate Analysis, 123:172–183, 2014. (Cited on page 537.)Google Scholar
[634] S. J., Lin. Stochastic analysis of fractional Brownian motions. Stochastics and Stochastics Reports, 55(1-2):121–140, 1995. (Cited on page 435.)Google Scholar
[635] G., Lindgren. Stationary Stochastic Processes. Chapman & Hall/CRC Texts in Statistical Science Series. Boca Raton, FL: CRC Press, 2013. Theory and applications. (Cited on pages 14 and 398.)
[636] M., Linn and A., Amirdjanova. Representations of the optimal filter in the context of nonlinear filtering of random fields with fractional noise. Stochastic Processes and their Applications, 119(8):2481–2500, 2009. (Cited on page 436.)Google Scholar
[637] M., Lippi and P., Zaffaroni. Aggregation of simple linear dynamics: exact asymptotics results. Econometrics Discussion Paper 350, STICERD-LSE, 1998. (Cited on page 223.)
[638] Br., Liseo, D., Marinucci, and L., Petrella. Bayesian semiparametric inference on long-range dependence. Biometrika, 88(4):1089–1104, 2001. (Cited on page 573.)Google Scholar
[639] B., Liu and D., Munson, Jr. Generation of a random sequence having a jointly specified marginal distribution and autocovariance. Acoustics, Speech and Signal Processing, IEEE Transactions on, 30(6):973–983, Dec 1982. (Cited on page 344.)
[640] J., Livsey, R., Lund, S., Kechagias and V., Pipiras. Multivariate count time series with flexible autocovariances. Preprint, 2016. (Cited on page 340.)
[641] I. N., Lobato. Consistency of the averaged cross-periodogram in long memory series. Journal of Time Series Analysis, 18(2):137–155, 1997. (Cited on page 536.)Google Scholar
[642] I. N., Lobato. A semiparametric two-step estimator in a multivariate long memory model. Journal of Econometrics, 90(1):129–153, 1999. (Cited on page 536.)Google Scholar
[643] I. N., Lobato and P. M., Robinson. A nonparametric test for I(0). Review of Economic Studies, 65(3):475–495, 1998. (Cited on page 536.)Google Scholar
[644] A., Lodhia, S., Sheffield, X., Sun and S. S., Watson. Fractional Gaussian fields: A survey. Probability Surveys, 13:1–56, 2016. (Cited on page 537.)Google Scholar
[645] L., López-Oliveros and S. I., Resnick. Extremal dependence analysis of network sessions. Extremes, 14(1):1–28, 2011. (Cited on page 121.)Google Scholar
[646] S. B., Lowen. Efficient generation of fractional Brownian motion for simulation of infrared focal-plane array calibration drift. Methodology and Computing in Applied Probability, 1 (4): 445–456, 1999. (Cited on page 112.)Google Scholar
[647] S. B., Lowen and M. C., Teich. Power-law shot noise. IEEE Transactions on Information Theory, IT-36(6):1302–1318, 1990. (Cited on page 225.)Google Scholar
[648] S. B., Lowen and M. C., Teich. Fractal-Based Point Processes. Wiley Series in Probability and Statistics. Hoboken, NJ: Wiley-Interscience [John Wiley & Sons], 2005. (Cited on pages 225 and 610.)
[649] A., Luceño. A fast likelihood approximation for vector general linear processes with long series: application to fractional differencing. Biometrika, 83(3):603–614, 1996. (Cited on page 570.)Google Scholar
[650] C., Ludeña and M., Lavielle. The Whittle estimator for strongly dependent stationary Gaussian fields. Scandinavian Journal of Statistics. Theory and Applications, 26(3):433–450, 1999. (Cited on page 537.)Google Scholar
[651] R. B., Lund, S. H., Holan, and J., Livsey. Long memory discrete-valued time series. In R. A., Davis, S. H., Holan, R., Lund, and N., Ravishanker, editors, Handbook of Discrete-Valued Time Series, pages 447–458. CRC Press, 2015. (Cited on page 611.)
[652] H., Luschgy and G., Pagès. Functional quantization of Gaussian processes. Journal of Functional Analysis, 196(2):486–531, 2002. (Cited on page 465.)Google Scholar
[653] H., Luschgy and G., Pagès. High-resolution product quantization for Gaussian processes under sup-norm distortion. Bernoulli, 13(3):653–671, 2007. (Cited on page 465.)Google Scholar
[654] H., Lütkepohl. New Introduction to Multiple Time Series Analysis. Berlin: Springer-Verlag, 2005. (Cited on page 470.)
[655] T., Lyons and Z., Qian. System Control and Rough Paths. Oxford Mathematical Monographs. Oxford: Oxford University Press, 2002. Oxford Science Publications. (Cited on page 435.)
[656] M., Lysy and N. S., Pillai. Statistical inference for stochastic differential equations with memory. Preprint, 2013. (Cited on page 436.)
[657] C., Ma. Correlation models with long-range dependence. Journal of Applied Probability, 39(2):370–382, 2002. (Cited on page 109.)Google Scholar
[658] C., Ma. Vector random fields with long-range dependence. Fractals, 19(2):249–258, 2011. (Cited on page 538.)Google Scholar
[659] C., Maccone. Eigenfunction expansion for fractional Brownian motions. Il Nuovo Cimento. B. Serie 11, 61(2):229–248, 1981. ISSN 0369-4100. (Cited on page 465.)Google Scholar
[660] C., Maccone. On the fractional Brownian motions BLH(t) and on the process B(t2H). Lettere al Nuovo Cimento. Rivista Internazionale della Società Italiana di Fisica. Serie 2, 36(2):33–34, 1983. (Cited on page 465.)Google Scholar
[661] M., Maejima. Some sojourn time problems for strongly dependent Gaussian processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 57:1–14, 1981. (Cited on page 343.)Google Scholar
[662] M., Maejima. Some limit theorems for sojourn times of strongly dependent Gaussian processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 60:359–380, 1982. (Cited on page 343.)Google Scholar
[663] M., Maejima. Sojourns of multidimensional Gaussian processes with dependent components. Yokohama Math. J., 33:121–130, 1985. (Cited on page 344.)Google Scholar
[664] M., Maejima. A remark on self-similar processes with stationary increments. The Canadian Journal of Statistics, 14(1):81–82, 1986. (Cited on pages 108 and 110.)Google Scholar
[665] M., Maejima. Some sojourn time problems for 2-dimensional Gaussian processes. Journal of Multivariate Analysis, 18:52–69, 1986. (Cited on page 344.)Google Scholar
[666] M., Maejima. Norming operators for operator-self-similar processes. In Stochastic Processes and Related Topics, Trends Math., pages 287–295. Boston, MA: Birkhäuser Boston, 1998. (Cited on page 536.)
[667] M., Maejima and J., Mason. Operator-self-similar stable processes. Stochastic Processes and their Applications, 54:139–163, 1994. (Cited on pages 476, 477, 478, 479, and 536.)Google Scholar
[668] M., Maejima and C. A., Tudor. Selfsimilar processes with stationary increments in the second Wiener chaos. Probability and Mathematical Statistics, 32(1):167–186, 2012. (Cited on page 281.)Google Scholar
[669] M., Maejima and C. A., Tudor. On the distribution of the Rosenblatt process. Statistics & Probability Letters, 83(6):1490–1495, 2013. (Cited on page 281.)Google Scholar
[670] M., Magdziarz. Correlation cascades, ergodic properties and long memory of infinitely divisible processes. Stochastic Processes and their Applications, 119(10):3416–3434, 2009. (Cited on page 111.)Google Scholar
[671] M., Magdziarz, A., Weron, K., Burnecki and J., Klafter. Fractional Brownian motion versus the continuous-time random walk: A simple test for subdiffusive dynamics. Physical Review Letters, 103(18):180602, 2009. (Cited on page 228.)Google Scholar
[672] P., Major. Multiple Wiener-Itô Integrals, volume 849 of Lecture Notes in Mathematics. Berlin: Springer, 1981. With applications to limit theorems. (Cited on pages 280 and 600.)
[673] P., Major. Multiple Wiener-Itô Integrals, volume 849 of Lecture Notes in Mathematics. Springer, Cham, second edition, 2014. With applications to limit theorems. (Cited on pages 280, 281, 584, and 610.)
[674] V., Makogin and Y., Mishura. Example of a Gaussian self-similar field with stationary rectangular increments that is not a fractional Brownian sheet. Stochastic Analysis and Applications, 33(3):413–428, 2015. (Cited on page 537.)Google Scholar
[675] S., Mallat. A Wavelet Tour of Signal Processing. Boston: Academic Press, 1998. (Cited on pages 443, 444, 450, and 451.)
[676] B. B., Mandelbrot. Long-run linearity, locally Gaussian processes, H-spectra and infinite variances. International Economic Review, 10:82–113, 1969. (Cited on page 224.)Google Scholar
[677] B. B., Mandelbrot. Intermittent turbulence in self-similar cascades; divergence of high moments and dimension of the carrier. Journal of Fluid Mechanics, 62:331–358, 1974. (Cited on page 612.)Google Scholar
[678] B. B., Mandelbrot. Limit theorems on the self-normalized range for weakly and strongly dependent processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 31:271–285, 1975. (Citedonpage 111.)Google Scholar
[679] B. B., Mandelbrot. The Fractal Geometry of Nature. New York: W. H. Freeman and Co., 1982. (Citedonpages 217 and 227.)
[680] B. B., Mandelbrot. A multifractal walk down Wall Street. Scientific American, pages 70–73, February 1999. (Cited on page 612.)
[681] B. B., Mandelbrot. The Fractalist. New York: Pantheon Books, 2012. Memoir of a scientific maverick, With an afterword by Michael Frame. (Cited on page xxii.)
[682] B. B., Mandelbrot and J. W., Van Ness. Fractional Brownian motions, fractional noises and applications. SIAM Review, 10:422–437, 1968. (Cited on pages 109, 110, 111, and 395.)Google Scholar
[683] B. B., Mandelbrot and J. R., Wallis. Noah, Joseph and operational hydrology. Water Resources Research, 4:909–918, 1968. (Cited on page 111.)Google Scholar
[684] B.B., Mandelbrot and J. R., Wallis. Computer experiments with fractional Gaussian noises, Parts 1, 2, 3. Water Resources Research, 5:228–267, 1969. (Cited on pages 109 and 111.)Google Scholar
[685] B. B., Mandelbrot and J. R., Wallis. Some long-run properties of geophysical records. Water Resources Research, 5:321–340, 1969. (Cited on page 111.)Google Scholar
[686] B. B., Mandelbrot and J. R., Wallis. Robustness of the rescaled range R/S in the measurement of noncyclic long-run statistical dependence. Water Resources Research, 5:967–988, 1969. (Cited on page 111.)Google Scholar
[687] M., Mandjes. Large Deviations for Gaussian Queues. John Wiley & Sons, Ltd., Chichester, 2007. Modelling Communication Networks. (Cited on page 611.)
[688] V. S., Mandrekar and L., Gawarecki. Stochastic analysis for Gaussian random processes and fields, volume 145 of Monographs on Statistics and Applied Probability. Boca Raton, FL: CRC Press, 2016. With applications. (Cited on page 436.)
[689] D., Marinucci and G., Peccati. Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications, volume 389. Cambridge University Press, 2011. (Cited on page 610.)
[690] D., Marinucci and P., M. Robinson. Alternative forms of fractional Brownian motion. Journal of Statistical Planning and Inference, 80(1-2):111–122, 1999. (Cited on page 110.)Google Scholar
[691] D., Marinucci and P., M. Robinson. Semiparametric fractional cointegration analysis. Journal of Econometrics, 105(1):225–247, 2001. (Cited on page 537.)Google Scholar
[692] T., Marquardt. Fractional Lévy processes with an application to long memory moving average processes. Bernoulli, 12(6):1099–1126, 2006. (Cited on page 110.)Google Scholar
[693] G., Maruyama. Nonlinear functionals of Gaussian stationary processes and their applications. In G., Maruyama and J.V., Prohorov, editors, Proceedings of the Third Japan-URSS symposium on probability theory, volume 550 of Lecture notes in Mathematics, pages 375–378, New York: Springer Verlag, 1976. (Cited on page 343.)
[694] G., Maruyama. Wiener functionals and probability limit theorems. I. The central limit theorems. Osaka Journal of Mathematics, 22(4):697–732, 1985. (Cited on page 343.)Google Scholar
[695] J., Mason. A comparison of the properties of operator-stable distributions and operator-self-similar processes. Colloquia Mathematica Societatis János Bolyai, 36:751–760, 1984. (Cited on page 536.)Google Scholar
[696] J., Mason and M., Xiao. Sample path properties of operator-self-similiar Gaussian random fields. Theory of Probability and its Applications, 46(1):58–78, 2002. (Cited on pages 536 and 537.)Google Scholar
[697] L., Massoulie and A., Simonian. Large buffer asymptotics for the queue with fractional Brownian input. Journal of Applied Probability, 36(3):894–906, 1999. (Cited on page 611.)Google Scholar
[698] M., Matsui and N.-R., Shieh. The Lamperti transforms of self-similar Gaussian processes and their exponentials. Stochastic Models, 30(1):68–98, 2014. (Cited on page 111.)Google Scholar
[699] K., Maulik, S., Resnick, and H., Rootzén. Asymptotic independence and a network traffic model. Journal of Applied Probability, 39(4):671–699, 2002. (Cited on page 224.)Google Scholar
[700] L., Mayoral. Heterogeneous dynamics, aggregation and the persistence of economic shocks. International Economic Review, 54(5):1295–1307, 2013. (Cited on page 224.)Google Scholar
[701] A., McCloskey and P., Perron. Memory parameter estimation in the presence of level shifts and deterministic trends. Econometric Theory, FirstView: 1–42, 10 2013. (Cited on pages 225 and 573.)Google Scholar
[702] B. M., McCoy. Advanced Statistical Mechanics, volume 146 of International Series of Monographs on Physics. Oxford: Oxford University Press, 2010. (Cited on pages 183 and 204.)
[703] B. M., McCoy and T. T., Wu. The Two-Dimensional Ising Model. Cambridge, MA: Harvard University Press, 1973. (Cited on pages 184, 187, 193, 194, 206, 209, 213, and 223.)
[704] T., McElroy and A., Jach. Tail index estimation in the presence of long-memory dynamics. Computational Statistics & Data Analysis, 56(2):266–282, 2012. (Cited on page 111.)Google Scholar
[705] T. S., McElroy and S. H., Holan. On the computation of autocovariances for generalized Gegenbauer processes. Statistica Sinica, 22(4):1661–1687, 2012. (Cited on page 110.)Google Scholar
[706] T. S., McElroy and S. H., Holan. Computation of the autocovariances for time series with multiple long-range persistencies. Computational Statistics and Data Analysis, 101:44–56, 2016. (Cited on page 110.)Google Scholar
[707] M. M., Meerschaert. Fractional calculus, anomalous diffusion, and probability. In Fractional dynamics, pages 265–284. Hackensack, NJ: World Sci. Publ., 2012. (Cited on page 396.)
[708] M. M., Meerschaert and F., Sabzikar. Stochastic integration for tempered fractional Brownian motion. Stochastic Processes and their Applications, 124(7):2363–2387, 2014. (Cited on page 395.)Google Scholar
[709] M. M., Meerschaert and H.-P., Scheffler. Spectral decomposition for operator self-similar processes and their generalized domains of attraction. Stochastic Processes and their Applications, 84(1):71–80, 1999. (Cited on page 536.)Google Scholar
[710] M. M., Meerschaert and H.-P., Scheffler. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. Wiley Series in Probability and Statistics. New York: John Wiley & Sons Inc., 2001. (Cited on pages 495, 510, 535, and 536.)
[711] M. M., Meerschaert and H.-P., Scheffler. Triangular array limits for continuous time random walks. Stochastic Processes and their Applications, 118(9):1606–1633, 2008. (Cited on page 227.)Google Scholar
[712] M. M., Meerschaert and A., Sikorskii. Stochastic Models for Fractional Calculus, volume 43 of de Gruyter Studies in Mathematics. Berlin: Walter de Gruyter & Co., 2012. (Cited on pages 352, 396, and 610.)
[713] M. M., Meerschaert, E., Nane and Y., Xiao. Correlated continuous time random walks. Statistics & Probability Letters, 79(9):1194–1202, 2009. (Cited on page 228.)Google Scholar
[714] F. G., Mehler. Ueber die Entwicklung einer Function von beliebig vielen Variablen nach Laplaceschen Functionen höherer Ordnung. Journal für die Reine und Angewandte Mathematik. [Crelle's Journal], 66:161–176, 1866. (Cited on page 342.)Google Scholar
[715] Y., Meyer. Wavelets and Operators, volume 37 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 1992. (Cited on pages 444 and 445.)
[716] Y., Meyer, F., Sellan and M. S., Taqqu. Wavelets, generalized white noise and fractional integration: the synthesis of fractional Brownian motion. The Journal of Fourier Analysis and Applications, 5(5):465–494, 1999. (Cited on pages 440, 445, 450, 452, 453, and 465.)Google Scholar
[717] T., Mikosch and G., Samorodnitsky. Scaling limits for cumulative input processes. Mathematics of Operations Research, 32(4):890–918, 2007. (Cited on page 224.)Google Scholar
[718] T., Mikosch and C., Stărică. Changes of structure in financial time series and the GARCH model. REVSTAT Statistical Journal, 2(1):41–73, 2004. (Cited on page 225.)Google Scholar
[719] T., Mikosch, S., Resnick, H., Rootzén, and A., Stegeman. Is network traffic approximated by stable Lévy motion or fractional Brownian motion? The Annals of Applied Probability, 12(1):23–68, 2002. (Cited on page 224.)Google Scholar
[720] J., Militk`y and S., Ibrahim. Complex characterization of yarn unevenness. In X., Zeng, Y., Li, D., Ruan, and L., Koehl, editors, Computational Textile, volume 55 of Studies in Computational Intelligence, pages 57–73. Berlin/Heidelberg: Springer, 2007. (Cited on page 225.)
[721] T. C., Mills. Time series modelling of two millennia of northern hemisphere temperatures: long memory or shifting trends? Journal of the Royal Statistical Society. Series A. Statistics in Society, 170(1):83–94, 2007. (Cited on pages 225 and 557.)Google Scholar
[722] Y. S., Mishura. Stochastic Calculus for Fractional Brownian Motion and Related Processes, volume 1929 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 2008. (Cited on pages 436 and 610.)
[723] Y. S., Mishura and G. M., Shevchenko. Rate of convergence of Euler approximations of solution to mixed stochastic differential equation involving Brownian motion and fractional Brownian motion. Random Operators and Stochastic Equations, 19(4):387–406, 2011. (Cited on page 436.)Google Scholar
[724] A., Moberg, D. M., Sonechkin, K., Holmgren, N. M., Datsenko, and W., Karlen. Highly variable northern hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature, 433:613–617, 2005. (Cited on page 557.)Google Scholar
[725] G. M., Molčan and Ju. I., Golosov. Gaussian stationary processes with asymptotically a power spectrum. Doklady Akademii Nauk SSSR, 184:546–549, 1969. (Cited on page 395.)Google Scholar
[726] G. M., Molchan. Gaussian processes with spectra which are asymptotically equivalent to a power of λ. Theory of Probability and Its Applications, 14:530–532, 1969. (Cited on page 395.)Google Scholar
[727] G. M., Molchan. Linear problems for fractional Brownian motion: a group approach. Theory of Probability and Its Applications, 47(1):69–78, 2003. (Cited on page 395.)Google Scholar
[728] J. F., Monahan. Numerical Methods of Statistics, 2nd edition. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press, 2011. (Cited on page 542.)
[729] A., Montanari. Longe range dependence in Hydrology. In P., Doukhan, G., Oppenheim, and M. S., Taqqu, editors, Theory and Applications of Long-range Dependence, pages 461–472. Birkhäuser, 2003. (Cited on page 111.)
[730] A., Montanari, R., Rosso and M. S., Taqqu. Some long-run properties of rainfall records in Italy. Journal of Geophysical Research – Atmospheres, 101(D23):431–438, 1996. (Cited on page 572.)Google Scholar
[731] A., Montanari, R., Rosso and M. S., Taqqu. Fractionally differenced ARIMA models applied to hydrologic time series: identification, estimation and simulation. Water Resources Research, 33:1035–1044, 1997. (Cited on page 111.)Google Scholar
[732] T., Mori and H., Oodaira. The law of the iterated logarithm for self-similar processes represented by multiple Wiener integrals. Probability Theory and Related Fields, 71(3):367–391, 1986. (Cited on page 281.)Google Scholar
[733] P., Mörters and Y., Peres. Brownian Motion. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press, 2010. With an appendix by Oded Schramm and Wendelin Werner. (Cited on page 14.)
[734] E., Moulines and P., Soulier. Broadband log-periodogram regression of time series with long-range dependence. The Annals of Statistics, 27(4):1415–1439, 1999. (Cited on page 573.)Google Scholar
[735] E., Moulines, F., Roueff and M. S., Taqqu. Central limit theorem for the log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context. Fractals, 15(4):301–313, 2007. (Cited on page 112.)Google Scholar
[736] E., Moulines, F., Roueff and M. S., Taqqu. On the spectral density of the wavelet coefficients of long-memory time series with application to the log-regression estimation of the memory parameter. Journal of Time Series Analysis, 28(2):155–187, 2007. (Cited on page 112.)Google Scholar
[737] E., Moulines, F., Roueff and M. S., Taqqu. A wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series. The Annals of Statistics, 36(4):1925–1956, 2008. (Cited on pages 112 and 574.)Google Scholar
[738] N., Naganuma. Asymptotic error distributions of the cranknicholson scheme for SDEs driven by fractional Brownian motion. Journal of Theoretical Probability, 28(3):1082–1124, 2015. (Cited on page 436.)Google Scholar
[739] M., Narukawa. On semiparametric testing of I(d) by FEXP models. Communications in Statistics. Theory and Methods, 42(9):1637–1653, 2013. (Cited on page 573.)Google Scholar
[740] M., Narukawa and Y., Matsuda. Broadband semi-parametric estimation of long-memory time series by fractional exponential models. Journal of Time Series Analysis, 32(2):175–193, 2011. (Cited on page 568.)Google Scholar
[741] A., Neuenkirch. Optimal approximation of SDE's with additive fractional noise. Journal of Complexity, 22(4):459–474, 2006. (Cited on page 436.)Google Scholar
[742] A., Neuenkirch. Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion. Stochastic Processes and their Applications, 118(12):2294–2333, 2008. (Cited on page 436.)Google Scholar
[743] A., Neuenkirch and I., Nourdin. Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion. Journal of Theoretical Probability, 20(4):871–899, 2007. (Cited on page 436.)Google Scholar
[744] A., Neuenkirch, I., Nourdin and S., Tindel. Delay equations driven by rough paths. Electronic Journal of Probability, 13: no. 67, 2031–2068, 2008. (Cited on page 436.)Google Scholar
[745] J. M., Nichols, C. C., Olson, J. V., Michalowicz, and F., Bucholtz. A simple algorithm for generating spectrally colored, non-Gaussian signals. Probabilistic Engineering Mechanics, 25(3):315–322, 2010. (Cited on page 344.)Google Scholar
[746] F. S., Nielsen. Local Whittle estimation of multi-variate fractionally integrated processes. Journal of Time Series Analysis, 32(3):317–335, 2011. (Cited on page 536.)Google Scholar
[747] M. Ø., Nielsen. Local empirical spectral measure of multivariate processes with long range dependence. Stochastic Processes and their Applications, 109(1):145–166, 2004. (Cited on page 536.)Google Scholar
[748] M. Ø., Nielsen. Local Whittle analysis of stationary fractional cointegration and the implied-realized volatility relation. Journal of Business & Economic Statistics, 25(4):427–446, 2007. (Cited on page 536.)Google Scholar
[749] M. Ø., Nielsen. Nonparametric cointegration analysis of fractional systems with unknown integration orders. Journal of Econometrics, 155(2):170–187, 2010. (Cited on page 537.)Google Scholar
[750] M. Ø., Nielsen and P., Frederiksen. Fully modified narrow-band least squares estimation of weak fractional cointegration. The Econometrics Journal, 14(1):77–120, 2011. (Cited on page 536.)Google Scholar
[751] M. Ø., Nielsen and P. H., Frederiksen. Finite sample comparison of parametric, semiparametric, and wavelet estimators of fractional integration. Econometric Reviews, 24(4):405–443, 2005. (Cited on page 571.)Google Scholar
[752] M., Niss. History of the Lenz-Ising model 1920–1950: from ferromagnetic to cooperative phenomena. Archive for History of Exact Sciences, 59(3):267–318, 2005. (Cited on page 227.)Google Scholar
[753] M., Niss. History of the Lenz-Ising model 1950–1965: from irrelevance to relevance. Archive for History of Exact Sciences, 63(3):243–287, 2009. (Cited on page 227.)Google Scholar
[754] D. J., Noakes, K. W., Hipel, A. I., McLeod, C., Jimenez, and S., Yakowitz. Forecasting annual geophysical time series. International Journal of Forecasting, 4(1):103–115, 1998. (Cited on page 572.)Google Scholar
[755] J. P., Nolan. Stable Distributions - Models for Heavy Tailed Data. Boston: Birkhauser, 2014. (Cited on page 111.)
[756] I., Norros. A storage model with self-similar input. Queueing Systems And Their Applications, 16:387–396, 1994. (Cited on page 611.)Google Scholar
[757] I., Norros and E., Saksman. Local independence of fractional Brownian motion. Stochastic Processes and their Applications, 119(10):3155–3172, 2009. (Cited on page 395.)Google Scholar
[758] I., Norros, E., Valkeila and J., Virtamo. An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli, 15:571–587, 1999. (Cited on page 395.)Google Scholar
[759] L., Nouira, M., Boutahar and V., Marimoutou. The effect of tapering on the semiparametric estimators for nonstationary long memory processes. Statistical Papers, 50(2):225–248, 2009. (Citedonpage 573.)Google Scholar
[760] I., Nourdin. Selected Aspects of Fractional Brownian Motion, volume 4 of Bocconi & Springer Series. Springer, Milan; Bocconi University Press, Milan, 2012. (Cited on pages 305, 343, 344, 436, and 610.)
[761] I., Nourdin and G., Peccati. Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields. The Annals of Probability, 37(6):2231–2261, 2009. (Cited on page 571.)Google Scholar
[762] I., Nourdin and G., Peccati. Stein's method on Wiener chaos. Probability Theory and Related Fields, 145(1-2):75–118, 2009. (Cited on pages 344 and 436.)Google Scholar
[763] I., Nourdin and G., Peccati. Normal Approximations with Malliavin Calculus, volume 192 of Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press, 2012. From Stein's Method to Universality. (Cited on pages 305, 343, 344, 426, 427, 435, 436, 604, and 610.)
[764] I., Nourdin and J., Rosiński. Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws. The Annals of Probability, 42(2):497–526, 2014. (Cited on pages 324 and 344.)Google Scholar
[765] I., Nourdin and T., Simon. On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion. Statistics & Probability Letters, 76(9):907–912, 2006. (Cited on pages 413, 414, 418, and 434.)Google Scholar
[766] I., Nourdin, D., Nualart and C. A., Tudor. Central and non-central limit theorems for weighted power variations of fractional Brownian motion. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 46(4):1055–1079, 2010. (Cited on page 280.)Google Scholar
[767] I., Nourdin, G., Peccati and G., Reinert. Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos. The Annals of Probability, 38(5):1947–1985, 2010. (Cited on page 343.)Google Scholar
[768] I., Nourdin, D., Nualart and G., Peccati. Strong asymptotic independence on Wiener chaos. Proceedings of the American Mathematical Society, 144(2):875–886, 2016. (Cited on pages 323 and 344.)Google Scholar
[769] D., Nualart. The Malliavin Calculus and Related Topics, 2nd edition. Probability and its Applications (New York). Berlin: Springer-Verlag, 2006. (Cited on pages 280, 408, 409, 412, 413, 414, 415, 436, 598, 600, 601, 602, 603, 604, 605, 606, 608, 609, and 610.)
[770] D., Nualart. Normal approximations with Malliavin calculus [book review of mr2962301]. American Mathematical Society. Bulletin. New Series, 51(3):491–497, 2014. (Cited on page 426.)Google Scholar
[771] D., Nualart and G., Peccati. Central limit theorems for sequences of multiple stochastic integrals. The Annals of Probability, 33(1):177–193, 2005. (Cited on pages 282, 305, 324, 343, 344, and 436.)Google Scholar
[772] D., Nualart and V., Pérez-Abreu. On the eigenvalue process of a matrix fractional Brownian motion. Stochastic Processes and their Applications, 124(12):4266–4282, 2014. (Cited on page 436.)Google Scholar
[773] D., Nualart and A. R, ăşcanu. Differential equations driven by fractional Brownian motion. Universitat de Barcelona. Collectanea Mathematica, 53(1):55–81, 2002. (Cited on page 413.)Google Scholar
[774] D., Nualart and B., Saussereau. Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion. Stochastic Processes and their Applications, 119(2):391–409, 2009. (Cited on pages 414 and 415.)Google Scholar
[775] C. J., Nuzman and H. V., Poor. Reproducing kernel Hilbert space methods for wide-sense self-similar processes. The Annals of Applied Probability, 11(4):1199–1219, 2001. (Cited on page 395.)Google Scholar
[776] G. L., O'Brien and W., Vervaat. Self-similar processes with stationary increments generated by point processes. The Annals of Probability, 13(1):28–52, 1985. (Cited on page 111.)Google Scholar
[777] B., Oğuz and V., Anantharam. Hurst index of functions of long-range-dependent Markov chains. Journal of Applied Probability, 49(2):451–471, 2012. (Cited on page 109.)Google Scholar
[778] A., Ohanissian, J. R., Russell, and R. S., Tsay. True or spurious long memory? A new test. Journal of Business & Economic Statistics, 26:161–175, 2008. (Cited on page 225.)Google Scholar
[779] L., Onsager. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. (2), 65:117–149, 1944. (Cited on page 226.)Google Scholar
[780] G., Oppenheim and M.-C., Viano. Aggregation of random parameters Ornstein-Uhlenbeck or AR processes: some convergence results. Journal of Time Series Analysis, 25(3):335–350, 2004. (Cited on page 223.)Google Scholar
[781] G., Oppenheim, M. Ould, Haye, and M.-C., Viano. Long memory with seasonal effects. Statistical Inference for Stochastic Processes, 3(1-2):53–68, 2000. 19th “Rencontres Franco-Belges de Statisticiens” (Marseille, 1998). (Cited on page 573.)Google Scholar
[782] S original by C., Fraley, U., Washington, Seattle. Rport by F. Leisch at TU Wien; since 2003-12: M. Maechler; fdGPH, fdSperio, etc by V. Reisen, and A. Lemonte. fracdiff: Fractionally differenced ARIMA aka ARFIMA(p, d, q) models, 2012. URL http://CRAN.R-project.org/package=fracdiff. R package version 1.4-2. (Cited on page 555.)
[783] M., Ossiander and E. C., Waymire. Statistical estimation for multiplicative cascades. The Annals of Statistics, 28(6):1533–1560, 2000. (Cited on page 612.)Google Scholar
[784] T., Owada and G., Samorodnitsky. Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows. The Annals of Probability, 43(1):240–285, 2015. (Cited on page 228.)Google Scholar
[785] J., Pai and N., Ravishanker. A multivariate preconditioned conjugate gradient approach for maximum likelihood estimation in vector long memory processes. Statistics & Probability Letters, 79(9):1282–1289, 2009. (Cited on page 570.)Google Scholar
[786] J., Pai and N., Ravishanker. Maximum likelihood estimation in vector long memory processes via EM algorithm. Computational Statistics & Data Analysis, 53(12):4133–4142, 2009. (Cited on page 570.)Google Scholar
[787] J. S., Pai and N., Ravishanker. Bayesian analysis of autoregressive fractionally integrated moving-average processes. Journal of Time Series Analysis, 19(1):99–112, 1998. (Cited on page 573.)Google Scholar
[788] R. E. A. C., Paley and N., Wiener. Fourier Transforms in the Complex Domain, volume 19. American Mathematical Soc., 1934. (Cited on page 456.)
[789] W., Palma. Long-Memory Time Series. NJ: Wiley Series in Probability and Statistics. Hoboken, Wiley-Interscience [John Wiley & Sons], 2007. Theory and Methods. (Cited on pages 43, 539, and 610.)
[790] W., Palma and N. H., Chan. Efficient estimation of seasonal long-range-dependent processes. Journal of Time Series Analysis, 26(6):863–892, 2005. (Cited on page 573.)Google Scholar
[791] A., Papavasiliou and C., Ladroue. Parameter estimation for rough differential equations. The Annals of Statistics, 39(4):2047–2073, 2011. (Cited on page 436.)Google Scholar
[792] J. C., Pardo and V., Rivero. Self-similar Markov processes. Sociedad Matemática Mexicana. Boletín. Tercera Serie, 19(2):201–235, 2013. (Cited on page 612.)Google Scholar
[793] C., Park, F., Godtliebsen, M. S., Taqqu, S., Stoev, and J. S., Marron. Visualization and inference based on wavelet coefficients, SiZer and SiNos. Computational Statistics & Data Analysis, 51(12):5994–6012, 2007. (Cited on page 112.)Google Scholar
[794] K., Park and W., Willinger, editors. Self-Similar Network Traffic and Performance Evaluation. J. Wiley & Sons, Inc., New York, 2000. (Cited on pages 224 and 610.)
[795] V., Paulauskas. On α-covariance, long, short and negative memories for sequences of random variables with infinite variance. Preprint, 2013. (Cited on page 111.)
[796] V., Paulauskas. Some remarks on definitions of memory for stationary random processes and fields. Preprint, 2016. (Cited on page 111.)
[797] G., Peccati and M. S., Taqqu. Wiener Chaos: Moments, Cumulants and Diagrams, volume 1 of Bocconi & Springer Series. Springer, 2011. (Cited on pages 242, 243, 245, 259, 265, 281, 305, 324, 343, 599, 600, 601, and 610.)
[798] G., Peccati and C., Tudor. Gaussian limits for vector-valued multiple stochastic integrals. Séminaire de Probabilités XXXVIII, pages 219–245, 2005. (Cited on page 344.)
[799] G., Peccati and C., Zheng. Multi-dimensional Gaussian fluctuations on the Poisson space. Electronic Journal of Probability, 15(48):1487–1527, 2010. (Cited on page 343.)Google Scholar
[800] M., Peligrad. Central limit theorem for triangular arrays of non-homogeneous Markov chains. Probability Theory and Related Fields, 154(3-4):409–428, 2012. (Cited on page 161.)Google Scholar
[801] M., Peligrad and H., Sang. Asymptotic properties of self-normalized linear processes with long memory. Econometric Theory, 28(3):548–569, 2012. (Cited on page 111.)Google Scholar
[802] M., Peligrad and H., Sang. Central limit theorem for linear processes with infinite variance. Journal of Theoretical Probability, 26(1):222–239, 2013. (Cited on page 111.)Google Scholar
[803] M., Peligrad and S., Sethuraman. On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion. ALEA. Latin American Journal of Probability and Mathematical Statistics, 4:245–255, 2008. (Cited on page 172.)Google Scholar
[804] R. F., Peltier and J. L., Véhel. Multifractional Brownian motion: definition and preliminary results. Technical Report 2645, Institut National de Recherche en Informatique et an Automatique, INRIA, Le Chesnay, France, 1995. (Cited on page 611.)
[805] L., Peng. Semi-parametric estimation of long-range dependence index in infinite variance time series. Statistics & Probability Letters, 51(2):101–109, 2001. (Cited on page 111.)Google Scholar
[806] D. B., Percival. Exact simulation of complex-valued Gaussian stationary processes via circulant embedding. Signal Processing, 86(7):1470–1476, 2006. (Cited on page 112.)Google Scholar
[807] E., Perrin, R., Harba, C., Berzin-Joseph, I., Iribarren, and A., Bonami. nth-Order fractional Brownian motion and fractional Gaussian noises. IEEE Transactions on Signal Processing, 49(5):1049–1059, 2001. (Cited on page 110.)Google Scholar
[808] A., Philippe, D., Surgailis, and M.-C., Viano. Almost periodically correlated processes with long memory. In Dependence in probability and statistics, volume 187 of Lecture Notes in Statist., pages 159–194. New York: Springer, 2006. (Cited on page 573.)
[809] J., Picard. Representation formulae for the fractional Brownian motion. In Séminaire de Probabilités XLIII, volume 2006 of Lecture Notes in Math., pages 3–70. Berlin: Springer, 2011. (Cited on page 395.)
[810] D., Pilipauskaitė and D., Surgailis. Scaling transition for nonlinear random fields with long-range dependence. To appear in Stochastic Processes and their Applications. Preprint, 2016. (Cited on page 537.)
[811] M. S., Pinsker and A. M., Yaglom. On linear extrapolation of random processes with stationary nth increments. Doklady Akad. Nauk SSSR (N.S.), 94:385–388, 1954. (Cited on page 110.)Google Scholar
[812] V., Pipiras. Wavelet-type expansion of the Rosenblatt process. The Journal of Fourier Analysis and Applications, 10(6):599–634, 2004. (Cited on page 465.)Google Scholar
[813] V., Pipiras. Wavelet-based simulation of fractional Brownian motion revisited. Applied and Computational Harmonic Analysis, 19(1):49–60, 2005. (Cited on pages 451, 454, and 465.)Google Scholar
[814] V., Pipiras and M. S., Taqqu. Convergence of the Weierstrass-Mandelbrot process to fractional Brownian motion. Fractals, 8:369–384, 2000. (Cited on page 227.)Google Scholar
[815] V., Pipiras and M. S., Taqqu. Integration questions related to fractional Brownian motion. Probability Theory and Related Fields, 118(2):251–291, 2000. (Cited on pages 358, 372, 374, 384, and 395.)Google Scholar
[816] V., Pipiras and M. S., Taqqu. The Weierstass-Mandelbrot process provides a series approximation to the harmonizable fractional stable motion. In C., Bandt, S., Graf, and M., Zähle, editors, Fractal Geometry and Stochastics II, pages 161–179. Birkhäuser, 2000. (Cited on page 227.)
[817] V., Pipiras and M. S., Taqqu. Are classes of deterministic integrands for fractional Brownian motion on an interval complete? Bernoulli, 7(6):873–897, 2001. (Cited on pages 364, 375, 377, and 395.)Google Scholar
[818] V., Pipiras and M. S., Taqqu. Deconvolution of fractional Brownian motion. Journal of Time Series Analysis, 23(4):487–501, 2002. (Cited on page 395.)Google Scholar
[819] V., Pipiras and M. S., Taqqu. Regularization and integral representations of Hermite processes. Statistics & Probability Letters, 80(23-24):2014–2023, 2010. (Cited on pages 241, 280, and 601.)Google Scholar
[820] V., Pipiras and M. S., Taqqu. Stable self-similar processes with stationary increments. Preprint, 2015. (Cited on pages 60, 63, 110, and 611.)
[821] V., Pipiras and M. S., Taqqu. Long-range dependence of the two-dimensional Ising model at critical temperature. In M., Frame and N., Cohen, editors, Benoit Mandelbrot: A Life in Many Dimensions, pages 399–440. World Scientific, 2015. (Cited on page 227.)
[822] V., Pipiras, M. S., Taqqu, and J. B., Levy. Slow, fast and arbitrary growth conditions for renewal reward processes when both the renewals and the rewards are heavy-tailed. Bernoulli, 10:121–163, 2004. (Cited on page 224.)Google Scholar
[823] E. J. G., Pitman and J., Pitman. A direct approach to the stable distributions. Advances in Applied Probability, 48(A):261–282, 2016. (Cited on page 585.)Google Scholar
[824] L. D., Pitt. Scaling limits of Gaussian vectors fields. Journal of Multivariate Analysis, 8(1):45–54, 1978. (Cited on page 536.)Google Scholar
[825] I., Podlubny. Fractional Differential Equations, volume 198 of Mathematics in Science and Engineering. San Diego, CA: Academic Press, Inc., 1999. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. (Cited on page 352.)
[826] I., Podlubny. Geometric and physical interpretation of fractional integration and fractional differentiation. Fractional Calculus & Applied Analysis, 5(4):367–386, 2002. Dedicated to the 60th anniversary of Prof. Francesco Mainardi. (Cited on page 395.)Google Scholar
[827] K., Polisano, M., Clausel, V., Perrier and L., Condat. Texture modeling by Gaussian fields with prescribed local orientation. In Image Processing (ICIP), 2014 IEEE International Conference on, pages 6091–6095, 2014. (Cited on page 537.)
[828] M., Polyak. Feynman diagrams for pedestrians and mathematicians. In Graphs and Patterns in Mathematics and Theoretical Physics, volume 73 of Proc. Sympos. Pure Math., pages 15–42. Providence, RI: Amer. Math. Soc., 2005. (Cited on page 281.)
[829] D. S., Poskitt. Properties of the sieve bootstrap for fractionally integrated and non-invertible processes. Journal of Time Series Analysis, 29(2):224–250, 2008. (Cited on page 574.)Google Scholar
[830] D. S., Poskitt, S. D., Grose, and G. M., Martin. Higher-order improvements of the sieve bootstrap for fractionally integrated processes. Journal of Econometrics, 188(1):94–110, 2015. (Cited on page 574.)Google Scholar
[831] B. L. S. Prakasa, Rao. Statistical Inference for Fractional Diffusion Processes. Wiley Series in Probability and Statistics. Chichester: John Wiley & Sons Ltd., 2010. (Cited on page 395.)
[832] R., Price. A useful theorem for nonlinear devices having Gaussian inputs. IRE Trans., IT-4:69–72, 1958. (Cited on page 333.)Google Scholar
[833] M. B., Priestley. Spectral Analysis and Time Series. Vol. 1. London-New York: Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], 1981. Univariate Series, Probability and Mathematical Statistics. (Cited on page 14.)
[834] P. E., Protter. Stochastic Integration and Differential Equations, 2nd edition, volume 21 of Stochastic Modelling and Applied Probability. Berlin: Springer-Verlag, 2005. Version 2.1, Corrected third printing. (Cited on pages 397 and 398.)
[835] D., Puplinskaitė and D., Surgailis. Scaling transition for long-range dependent Gaussian random fields. Stochastic Processes and their Applications, 125(6):2256–2271, 2015. (Cited on pages 529 and 537.)Google Scholar
[836] D., Puplinskaitė and D., Surgailis. Aggregation of autoregressive random fields and anisotropic long-range dependence. Bernoulli, 22(4):2401–2441, 2016. (Cited on page 537.)Google Scholar
[837] Z., Qu. A test against spurious long memory. Journal of Business and Economic Statistics, 29(9):423–438, 2011. (Cited on pages 225 and 573.)Google Scholar
[838] R Core, Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing, 2013. URL www.R-project.org/. (Citedonpage 555.)
[839] S. T., Rachev and S., Mittnik. Stable Paretian Models in Finance. New York: Wiley, 2000. (Cited on page 111.)
[840] B. S., Rajput and J., Rosiński. Spectral representation of infinitely divisible processes. Probability Theory and Related Fields, 82: 451–487, 1989. (Cited on pages 594, 595, and 597.)Google Scholar
[841] G., Rangarajan and M., Ding. Processes with Long-Range Correlations: Theory and Applications, volume 621. Springer Science & Business Media, 2003. (Cited on pages 228 and 610.)
[842] B. L. S. P., Rao. Statistical Inference for Fractional Diffusion Processes. Wiley Series in Probability and Statistics. Wiley, 2011. (Cited on page 610.)
[843] V., Reisen, B., Abraham and S., Lopes. Estimation of parameters in ARFIMA processes: a simulation study. Communications in Statistics. Simulation and Computation, 30(4):787–803, 2001. (Cited on page 571.)Google Scholar
[844] V. A., Reisen, A. L., Rodrigues, and W., Palma. Estimating seasonal long-memory processes: a Monte Carlo study. Journal of Statistical Computation and Simulation, 76 (4):305–316, 2006. (Citedonpage 573.)Google Scholar
[845] S., Resnick. Adventures in Stochastic Processes. Boston, MA: Birkhäuser Boston Inc., 1992. (Cited on page 87.)
[846] S. I., Resnick. A Probability Path. Boston, MA: Birkhäuser Boston Inc., 1999. (Cited on page 68.)
[847] S. I., Resnick. Heavy-Tail Phenomena. Springer Series in Operations Research and Financial Engineering. New York: Springer, 2007. Probabilistic and statistical modeling. (Cited on page 129.)
[848] D., Revuz and M., Yor. Continuous Martingales and Brownian Motion. Berlin: Springer-Verlag, 1999. (Cited on page 398.)
[849] R. H., Riedi. Multifractal processes. In Theory and applications of long-range dependence, pages 625–716. Boston, MA: Birkhäuser Boston, 2003. (Cited on page 612.)
[850] F., Riesz and B. Sz.-, Nagy. Functional Analysis. New York: Frederick Ungar Publishing Co., 1955. Translated by Leo F., Boron. (Cited on page 438.)
[851] P. M., Robinson. Statistical inference for a random coefficient autoregressive model. Scandinavian Journal of Statistics. Theory and Applications, 5(3):163–168, 1978. (Cited on page 223.)Google Scholar
[852] P. M., Robinson. Log-periodogram regression of time series with long range dependence. The Annals of Statistics, 23(3):1048–1072, 1995. (Cited on pages 93, 111, and 536.)Google Scholar
[853] P. M., Robinson. Gaussian semiparametric estimation of long range dependence. The Annals of Statistics, 23:1630–1661, 1995. (Cited on pages 560, 561, and 572.)Google Scholar
[854] P. M., Robinson. Time Series with Long Memory. Advanced texts in econometrics. Oxford University Press, 2003. (Cited on page 610.)
[855] P. M., Robinson. Multiple local Whittle estimation in stationary systems. The Annals of Statistics, 36(5):2508–2530, 2008. (Cited on page 536.)Google Scholar
[856] P. M., Robinson and M., Henry. Higher-order kernel semiparametric M-estimation of long memory. Journal of Econometrics, 114(1):1–27, 2003. (Cited on page 572.)Google Scholar
[857] P. M., Robinson and D., Marinucci. Semiparametric frequency domain analysis of fractional coin-tegration. In P. M., Robinson, editor, Time Series with Long Memory. Oxford: Oxford University Press, 2003. (Cited on page 536.)
[858] P. M., Robinson and Y., Yajima. Determination of cointegrating rank in fractional systems. Journal of Econometrics, 106(2):217–241, 2002. (Cited on pages 536 and 537.)Google Scholar
[859] L. C. G., Rogers. Arbitrage with fractional Brownian motion. Mathematical Finance, 7:95–105, 1997. (Cited on page 435.)Google Scholar
[860] M., Rosenblatt. Independence and dependence. In Proceedings of the 4th Berkeley Symposium Mathematical Statistics and Probability, pages 431–443. University of California Press, 1961. (Cited on pages 110, 281, 343, and 612.)
[861] M., Rosenblatt. Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 49:125–132, 1979. (Cited on page 343.)Google Scholar
[862] W. A., Rosenkrantz and J., Horowitz. The infinite source model for internet traffic: statistical analysis and limit theorems. Methods and Applications of Analysis, 9(3):445–461, 2002. Special issue dedicated to Daniel W. Stroock and Srinivasa S. R. Varadhan on the occasion of their 60th birthday. (Cited on page 224.)Google Scholar
[863] H., Rost and M. E., Vares. Hydrodynamics of a one-dimensional nearest neighbor model. In Particle systems, random media and large deviations (Brunswick, Maine, 1984), volume 41 of Contemp. Math., pages 329–342. Providence, RI: Amer. Math. Soc., 1985. (Cited on page 168.)
[864] S., Rostek. Option Pricing in Fractional Brownian Markets, volume 622 of Lecture Notes in Economics and Mathematical Systems. Berlin: Springer-Verlag, Berlin, 2009. With a foreword by Rainer Schöbel. (Cited on page 436.)
[865] G.-C., Rota and T. C., Wallstrom. Stochastic integrals: a combinatorial approach. The Annals of Probability, 25(3):1257–1283, 1997. (Cited on page 281.)Google Scholar
[866] F., Roueff and M. S., Taqqu. Asymptotic normality of wavelet estimators of the memory parameter for linear processes. Journal of Time Series Analysis, 30(5):534–558, 2009. (Cited on page 112.)Google Scholar
[867] F., Roueff and M. S., Taqqu. Central limit theorems for arrays of decimated linear processes. Stochastic Processes and their Applications, 119(9):3006–3041, 2009. (Cited on page 112.)Google Scholar
[868] F., Roueff and R., von Sachs. Locally stationary long memory estimation. Stochastic Processes and their Applications, 121(4):813–844, 2011. (Cited on page 573.)Google Scholar
[869] M., Roughan and D., Veitch. Measuring long-range dependence under changing traffic conditions. In Proceedings of IEEE INFOCOM, volume 3, pages 1513–1521, Mar 1999. (Cited on page 225.)Google Scholar
[870] M., Roughan, D., Veitch and P., Abry. Real-time estimation of the parameters of long-range dependence. IEEE/ACM Transactions on Networking (TON), 8(4):467–478, 2000. (Cited on page 112.)Google Scholar
[871] S. G., Roux, M., Clausel, B., Vedel, S., Jaffard and P., Abry. Self-similar anisotropic texture analysis: the hyperbolic wavelet transform contribution. IEEE Transactions on Image Processing, 22(11):4353–4363, 2013. (Cited on page 537.)Google Scholar
[872] A., Roy, T. S., McElroy, and P., Linton. Estimation of causal invertible VARMA models. Preprint, 2014. (Cited on page 570.)
[873] F., Russo and C. A., Tudor. On bifractional Brownian motion. Stochastic Processes and their Applications, 116(5):830–856, 2006. (Cited on page 110.)Google Scholar
[874] A. A., Ruzmaikina. Stieltjes integrals of Hölder continuous functions with applications to fractional Brownian motion. Journal of Statistical Physics, 100(5-6):1049–1069, 2000. (Cited on page 435.)Google Scholar
[875] F., Sabzikar. Tempered Hermite process. Modern Stochastics. Theory and Applications, 2:327–341, 2015. (Cited on page 344.)Google Scholar
[876] A., Sakai. Lace expansion for the Ising model. Communications in Mathematical Physics, 272(2):283–344, 2007. (Cited on page 227.)Google Scholar
[877] A., Samarov and M. S., Taqqu. On the efficiency of the sample mean in long memory noise. Journal of Time Series Analysis, 9:191–200, 1988. (Cited on page 540.)Google Scholar
[878] S. G., Samko, A. A., Kilbas, and O. I., Marichev. Fractional Integrals and Derivatives. Yverdon: Gordon and Breach Science Publishers, 1993. Theory and Applications. (Cited on pages 348, 354, 356, 357, 359, 376, 377, 379, 381, 395, 401, and 406.)
[879] G., Samorodnitsky. Long range dependence. Foundations and Trends[circleR] in Stochastic Systems, 1(3):163–257, 2006. (Cited on pages 27, 77, 107, and 610.)Google Scholar
[880] G., Samorodnitsky. Stochastic Processes and Long Range Dependence. Springer, 2016. (Cited on page 610.)
[881] G., Samorodnitsky and M. S., Taqqu. The various linear fractional Lévy motions. In T. W., Anderson, K. B., Athreya, and D. L., Iglehart, editors, Probability, Statistics and Mathematics: Papers in Honor of Samuel Karlin, pages 261–270, Boston: Academic Press, 1989. (Cited on page 110.)
[882] G., Samorodnitsky and M. S., Taqqu. Linear models with long-range dependence and finite or infinite variance. In D., Brillinger, P., Caines, J., Geweke, E., Parzen, M., Rosenblatt, and M. S., Taqqu, editors, New Directions in Time Series Analysis, Part II, pages 325–340. IMA Volumes in Mathematics and its Applications, Volume 46, New York: Springer-Verlag, 1992. (Cited on page 110.)
[883] G., Samorodnitsky and M. S., Taqqu. Stable Non-Gaussian Random Processes. Stochastic Modeling. New York: Chapman & Hall, 1994. Stochastic models with infinite variance. (Cited on pages 61, 62, 83, 84, 585, 592, 593, 595, and 596.)
[884] M. V., Sánchez de Naranjo. Non-central limit theorems for nonlinear functionals of k Gaussian fields. Journal of Multivariate Analysis, 44(2):227–255, 1993. (Cited on page 344.)Google Scholar
[885] M. V., Sánchez de Naranjo. A central limit theorem for non-linear functionals of stationary Gaussian vector processes. Statistics & Probability Letters, 22(3):223–230, 1995. (Cited on page 344.)Google Scholar
[886] K.-i., Sato. Lévy Processes and Infinitely Divisible Distributions, volume 68 of Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge University Press, 2013. Translated from the 1990 Japanese original, Revised edition of the 1999 English translation. (Cited on page 596.)
[887] A., Scherrer, N., Larrieu, P., Owezarski, P., Borgnat and P., Abry. Non-Gaussian and long memory statistical characterizations for internet traffic with anomalies. Dependable and Secure Computing, IEEE Transactions on, 4(1):56–70, 2007. (Cited on pages 344 and 572.)Google Scholar
[888] M., Schlather. Some covariance models based on normal scale mixtures. Bernoulli, 16(3):780–797, 2010. (Cited on page 530.)Google Scholar
[889] M., Schlather. Construction of covariance functions and unconditional simulation of random fields. In E., Porcu, J. M., Montero, and M., Schlather, editors, Advances and Challenges in Space-time Modelling of Natural Events, Lecture Notes in Statistics, pages 25–54. Berlin, Heidelberg: Springer, 2012. (Cited on page 538.)
[890] I. J., Schoenberg. Metric spaces and completely monotone functions. Annals of Mathematics. Second Series, 39(4):811–841, 1938. (Cited on page 530.)Google Scholar
[891] H., Schönfeld. Beitrag zum 1/f-gesetz beim rauschen von halbleitern. Zeitschrift für Naturforschung A, 10 (4): 291–300, 1955. (Cited on page 225.)Google Scholar
[892] O., Schramm. Scaling limits of loop-erased random walks and uniform spanning trees. Israel Journal of Mathematics, 118:221–288, 2000. ISSN 0021-2172. (Cited on page 227.)Google Scholar
[893] K. J., Schrenk, N., Posé, J. J., Kranz, L. V. M., van Kessenich, N. A. M., Araújo, and H. J., Herrmann. Percolation with long-range correlated disorder. Physical Review E, 88(5):052102, 2013. (Cited on page 227.)Google Scholar
[894] G., Schwarz. Estimating the dimension of a model. The Annals of Statistics, 6(2):461–464, 1978. (Citedonpage 552.)Google Scholar
[895] S scripts originally by J., Beran; Datasets via B. Whitcher Toplevel R functions and much more by M. Maechler. longmemo: Statistics for Long-Memory Processes (Jan Beran) – Data and Functions, 2011. URL http://CRAN.R-project.org/package=longmemo. R package version 1.0-0. (Cited on page 572.)
[896] R. J., Sela and C. M., Hurvich. Computationally efficient methods for two multivariate fractionally integrated models. Journal of Time Series Analysis, 30(6):631–651, 2009. (Cited on page 570.)Google Scholar
[897] R. J., Sela and C. M., Hurvich. The averaged periodogram estimator for a power law in coherency. Journal of Time Series Analysis, 33(2):340–363, 2012. (Cited on page 537.)Google Scholar
[898] K., Sen, P., Preuss and H., Dette. Measuring stationarity in long-memory processes. To appear in Statistica Sinica. Preprint, 2013. (Cited on page 573.)
[899] S., Sethuraman. Diffusive variance for a tagged particle in d ≤ 2 asymmetric simple exclusion. ALEA. Latin American Journal of Probability and Mathematical Statistics, 1:305–332, 2006. (Citedonpage 226.)Google Scholar
[900] S., Sethuraman, S. R. S., Varadhan, and H.-T., Yau. Diffusive limit of a tagged particle in asymmetric simple exclusion processes. Communications on Pure and Applied Mathematics, 53(8):972–1006, 2000. (Cited on page 226.)Google Scholar
[901] X., Shao. Self-normalization for time series: a review of recent developments. Journal of the American Statistical Association, 110(512):1797–1817, 2015. (Cited on page 574.)Google Scholar
[902] X., Shao and W. B., Wu. Local Whittle estimation of fractional integration for nonlinear processes. Econometric Theory, 23(5):899–929, 2007. (Cited on pages 573 and 611.)Google Scholar
[903] O., Sheluhin, S., Smolskiy and A., Osin. Self-Similar Processes in Telecommunications. Wiley, 2007. (Cited on pages 224 and 610.)
[904] M., Sherman. Spatial Statistics and Spatio-Temporal Data. Wiley Series in Probability and Statistics. Chichester: John Wiley & Sons Ltd., 2011. Covariance functions and directional properties. (Cited on page 538.)
[905] K., Shimotsu. Gaussian semiparametric estimation of multivariate fractionally integrated processes. Journal of Econometrics, 137(2):277–310, 2007. (Cited on page 536.)Google Scholar
[906] K., Shimotsu. Exact local Whittle estimation of fractionally cointegrated systems. Journal of Econometrics, 169(2):266–278, 2012. (Cited on page 537.)Google Scholar
[907] K., Shimotsu and P. C. B., Phillips. Exact local Whittle estimation of fractional integration. The Annals of Statistics, 33 (4): 1890–1933, 2005. (Cited on page 572.)Google Scholar
[908] K., Shimotsu and P. C. B., Phillips. Local Whittle estimation of fractional integration and some of its variants. Journal of Econometrics, 130(2):209–233, 2006. (Cited on page 572.)Google Scholar
[909] R. H., Shumway and D. S., Stoffer. Time Series Analysis and Its Applications, 3rd edition. Springer Texts in Statistics. New York: Springer, 2011. With R examples. (Cited on page 14.)
[910] E. V., Slud. The moment problem for polynomial forms in normal random variables. The Annals of Probability, 21(4):2200–2214, 1993. (Cited on pages 280 and 281.)Google Scholar
[911] A., Sly and C., Heyde. Nonstandard limit theorem for infinite variance functionals. The Annals of Probability, 36(2):796–805, 2008. (Cited on page 343.)Google Scholar
[912] S., Smirnov. Conformal invariance in random cluster models. II. Scaling limit of the interface. Annals of Mathematics, 172(2):1453–1467, 2010. (Cited on page 227.)Google Scholar
[913] A., Smith. Level shifts and the illusion of long memory in economic time series. Journal of Business & Economic Statistics, 23(3):321–335, 2005. (Cited on page 225.)Google Scholar
[914] P. J., Smith. A recursive formulation of the old problem of obtaining moments from cumulants and vice versa. The American Statistician, 49(2):217–218, 1995. (Cited on page 265.)Google Scholar
[915] T., Sottinen. On Gaussian processes equivalent in law to fractional Brownian motion. Journal of Theoretical Probability, 17(2):309–325, 2004. (Cited on page 395.)Google Scholar
[916] P., Soulier. Best attainable rates of convergence for the estimation of the memory parameter. In Dependence in probability and statistics, volume 200 of Lecture Notes in Statist, pages 43–57. Berlin: Springer, 2010. (Cited on page 572.)
[917] F., Sowell. Fractionally integrated vector time series. Ph.D. dissertation, Duke University, 1986. (Cited on page 537.)
[918] F. B., Sowell. Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics, 53:165–188, 1992. (Cited on pages 539, 570, and 571.)Google Scholar
[919] F., Spitzer. Uniform motion with elastic collision of an infinite particle system. Journal of Mathematics and Mechanics, 18:973–989, 1968/1969. (Cited on pages 163 and 225.)
[920] M. L., Stein. Local stationarity and simulation of self-affine intrinsic random functions. IEEE Transactions on Information Theory, 47 (4): 1385–1390, 2001. (Cited on page 112.)Google Scholar
[921] M. L., Stein. Fast and exact simulation of fractional Brownian surfaces. Journal of Computational and Graphical Statistics, 11(3):587–599, 2002. (Cited on page 112.)Google Scholar
[922] M. L., Stein. Simulation of Gaussian random fields with one derivative. Journal of Computational and Graphical Statistics, 21(1):155–173, 2012. (Cited on page 112.)Google Scholar
[923] F. W., Steutel and K. van, Harn. Infinite Divisibility of Probability Distributions on the Real Line, volume 259 of Monographs and Textbooks in Pure and Applied Mathematics. New York: Marcel Dekker, Inc., 2004. (Cited on page 596.)
[924] S., Stoev and M. S., Taqqu. Wavelet estimation for the Hurst parameter in stable processes. In G., Rangarajan and M., Ding, editors, Processes with Long-Range Correlations: Theory and Applications, pages 61–87, Berlin: Springer-Verlag, 2003. Lecture Notes in Physics 621. (Cited on page 112.)
[925] S., Stoev and M. S., Taqqu. Stochastic properties of the linear multifractional stable motion. Advances in Applied Probability, 36(4):1085–1115, 2004. (Cited on pages 110 and 611.)Google Scholar
[926] S., Stoev and M. S., Taqqu. Simulation methods for linear fractional stable motion and FARIMA using the fast Fourier transform. Fractals, 12(1):95–121, 2004. (Cited on pages 61 and 82.)Google Scholar
[927] S., Stoev and M. S., Taqqu. Asymptotic self-similarity and wavelet estimation for long-range dependent FARIMA time series with stable innovations. Journal of Time Series Analysis, 26(2):211–249, 2005. (Cited on page 112.)Google Scholar
[928] S., Stoev and M. S., Taqqu. Path properties of the linear multifractional stable motion. Fractals, 13(2):157–178, 2005. (Cited on pages 110 and 611.)Google Scholar
[929] S., Stoev, M. S., Taqqu, C., Park, G., Michailidis, and J. S., Marron. LASS: a tool for the local analysis of self-similarity. Computational Statistics and Data Analysis, 50(9):2447–2471, 2006. (Cited on page 112.)Google Scholar
[930] S. A., Stoev and M. S., Taqqu. How rich is the class of multifractional Brownian motions? Stochastic Processes and their Applications, 116(2):200–221, 2006. (Cited on page 611.)Google Scholar
[931] T. C., Sun. A central limit theorem for non-linear functions of a normal stationary process. Journal of Mathematics and Mechanics, 12:945–978, 1963. (Cited on page 343.)Google Scholar
[932] T. C., Sun. Some further results on central limit theorems for non-linear functions of a normal stationary process. Journal of Mathematics and Mechanics, 14:71–85, 1965. (Cited on page 343.)Google Scholar
[933] X., Sun and F., Guo. On integration by parts formula and characterization of fractional OrnsteinUhlenbeck process. Statistics & Probability Letters, 107:170–177, 2015. (Cited on page 395.)Google Scholar
[934] D., Surgailis. Convergence of sums of nonlinear functions of moving averages to self-similar processes. Doklady Akademii Nauk SSSR, 257(1):51–54, 1981. (Cited on page 343.)Google Scholar
[935] D., Surgailis. Zones of attraction of self-similar multiple integrals. Litovsk. Mat. Sb., 22(3):185–201, 1982. (Cited on pages 307, 309, 311, and 343.)Google Scholar
[936] D., Surgailis. Long-range dependence and Appell rank. The Annals of Probability, 28(1):478–497, 2000. (Cited on page 343.)Google Scholar
[937] D., Surgailis. CLTs for polynomials of linear sequences: diagram formula with illustrations. In Theory and Applications of Long-Range Dependence, pages 111–127. Boston, MA: Birkhäuser Boston, 2003. (Cited on pages 244 and 343.)
[938] D., Surgailis and M., Vaičiulis. Convergence of Appell polynomials of long range dependent moving averages in martingale differences. Acta Applicandae Mathematicae, 58(1-3):343–357, 1999. Limit theorems of probability theory (Vilnius, 1999). (Cited on page 343.)Google Scholar
[939] G., Szegö. On certain Hermitian forms associated with the Fourier series of a positive function. Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.], 1952 (Tome Supplementaire): 228–238, 1952. (Cited on page 211.)Google Scholar
[940] A.-S., Sznitman. Topics in random walks in random environment. In School and Conference on Probability Theory, ICTP Lect. Notes, XVII, pages 203–266 (electronic). Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004. (Cited on page 178.)
[941] J., Szulga and F., Molz. The Weierstrass-Mandelbrot process revisited. Journal of Statistical Physics, 104(5-6):1317–1348, 2001. (Cited on page 227.)Google Scholar
[942] P. D., Tafti and M., Unser. Fractional Brownian vector fields. Multiscale Modeling & Simulation. A SIAM Interdisciplinary Journal, 8(5):1645–1670, 2010. (Cited on page 538.)Google Scholar
[943] M. S., Taqqu. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 31:287–302, 1975. (Cited on pages 110, 281, and 343.)Google Scholar
[944] M. S., Taqqu. Law of the iterated logarithm for sums of non-linear functions of the Gaussian variables that exhibit a long range dependence. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 40:203–238, 1977. (Cited on pages 279 and 281.)Google Scholar
[945] M. S., Taqqu. Convergence of integrated processes of arbitrary Hermite rank. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 50:53–83, 1979. (Cited on pages 280 and 343.)Google Scholar
[946] M. S., Taqqu. The Rosenblatt process. In R. A., Davis, K.-., Lii, and D. N., Politis, editors, Selected Works of Murray Rosenblatt, Selected Works in Probability and Statistics, pages 29–45. New York: Springer, 2011. (Cited on page 281.)
[947] M. S., Taqqu and J., Levy. Using renewal processes to generate long-range dependence and high variability. In E., Eberlein and M. S., Taqqu, editors, Dependence in Probability and Statistics, pages 73–89, Boston: Birkhäuser, 1986. (Cited on page 224.)
[948] M. S., Taqqu and V., Teverovsky. Semi-parametric graphical estimation techniques for long-memory data. In P. M., Robinson and M., Rosenblatt, editors, Athens Conference on Applied Probability and Time Series Analysis. Volume II: Time Series Analysis in Memory of E. J. Hannan, volume 115 of Lecture Notes in Statistics, pages 420–432, New York: Springer-Verlag, 1996. (Cited on page 574.)
[949] M. S., Taqqu and V., Teverovsky. Robustness of Whittle-type estimates for time series with long-range dependence. Stochastic Models, 13:723–757, 1997. (Cited on page 571.)Google Scholar
[950] M. S., Taqqu and R., Wolpert. Infinite variance self-similar processes subordinate to a Poisson measure. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 62:53–72, 1983. (Cited on page 111.)Google Scholar
[951] M. S., Taqqu, V., Teverovsky and W., Willinger. Estimators for long-range dependence: an empirical study. Fractals, 3 (4): 785–798, 1995. Reprinted in Fractal Geometry and Analysis, C.J.G. Evertsz, H.-O. Peitgen and R. F. Voss, editors. Singapore: World Scientific Publishing Co., 1996. (Cited on page 574.)Google Scholar
[952] M. S., Taqqu, W., Willinger and R., Sherman. Proof of a fundamental result in self-similar traffic modeling. Computer Communications Review, 27(2):5–23, 1997. (Cited on page 224.)Google Scholar
[953] M., Tayefi and T., V. Ramanathan. An overview of FIGARCH and related time series models. Austrian Journal of Statistics, 41(3):175–196, 2012. (Cited on page 611.)Google Scholar
[954] G., Terdik. Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis: A Frequency Domain Approach, volume 142. Springer Science & Business Media, 1999. (Cited on page 610.)
[955] G., Terdik. Long range dependence in third order for non-Gaussian time series. In Advances in directional and linear statistics, pages 281–304. Heidelberg: Physica-Verlag/Springer, 2011. (Cited on page 109.)
[956] A. H., Tewfik and M., Kim. Correlation structure of the discrete wavelet coefficients of fractional Brownian motions. IEEE Transactions on Information Theory, IT-38(2):904–909, 1992. (Cited on page 112.)Google Scholar
[957] G., Teyssière and P., Abry. Wavelet analysis of nonlinear long-range dependent processes. Applications to financial time series. In Long Memory in Economics, pages 173–238. Berlin: Springer, 2007. (Cited on page 112.)
[958] G., Teyssière and A. P., Kirman. Long Memory in Economics. Berlin, Heidelberg: Springer 2006. (Cited on page 610.)
[959] S., Tindel, C. A., Tudor, and F., Viens. Stochastic evolution equations with fractional Brownian motion. Probability Theory and Related Fields, 127(2):186–204, 2003. (Cited on page 436.)Google Scholar
[960] S., Torres, C. A., Tudor, and F. G., Viens. Quadratic variations for the fractional-colored stochastic heat equation. Electronic Journal of Probability, 19: no. 76, 51, 2014. (Cited on page 227.)Google Scholar
[961] W.-J., Tsay. Maximum likelihood estimation of stationary multivariate ARFIMA processes. Journal of Statistical Computation and Simulation, 80(7-8):729–745, 2010. (Cited on page 570.)Google Scholar
[962] C. A., Tudor. Analysis of the Rosenblatt process. ESAIM. Probability and Statistics, 12:230–257, 2008. (Cited on page 280.)Google Scholar
[963] C. A., Tudor. Analysis of Variations for Self-Similar Processes. Probability and its Applications (New York). Springer, Cham, 2013. A Stochastic Calculus Approach. (Cited on pages 343, 436, and 610.)
[964] C. A., Tudor and F. G., Viens. Statistical aspects of the fractional stochastic calculus. The Annals of Statistics, 35(3):1183–1212, 2007. (Cited on page 436.)Google Scholar
[965] C. A., Tudor and Y., Xiao. Sample path properties of bifractional Brownian motion. Bernoulli, 13(4):1023–1052, 2007. (Cited on page 110.)Google Scholar
[966] C. A., Tudor and Y., Xiao. Sample paths of the solution to the fractional-colored stochastic heat equation. Stochastics and Dynamics, 17(1):1750004, 2017. (Cited on page 227.)Google Scholar
[967] V. V., Uchaikin and V. M., Zolotarev. Chance and Stability. Modern Probability and Statistics. Utrecht: VSP, 1999. Stable distributions and their applications, With a foreword by V. Yu. Korolev and Zolotarev. (Cited on pages 111 and 227.)
[968] M., Unser and T., Blu. Cardinal exponential splines. I. Theory and filtering algorithms. IEEE Transactions on Signal Processing, 53(4):1425–1438, 2005. (Cited on page 465.)Google Scholar
[969] M., Unser and T., Blu. Self-similarity. I. Splines and operators. IEEE Transactions on Signal Processing, 55(4):1352–1363, 2007. (Cited on page 465.)Google Scholar
[970] A., Van der Ziel. Flicker noise in electronic devices. Advances in Electronics and Electron Physics, 49:225–297, 1979. (Cited on page 225.)Google Scholar
[971] K., van Harn and F. W., Steutel. Integer-valued self-similar processes. Communications in Statistics. Stochastic Models, 1(2):191–208, 1985. (Cited on page 110.)Google Scholar
[972] H., van Zanten. Comments on “PCA based Hurst exponent estimator for fBm signals under disturbances”. IEEE Transactions on Signal Processing, 58(8):4466–4467, 2010. (Cited on page 464.)Google Scholar
[973] S. R. S., Varadhan. Self-diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion. Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 31(1):273–285, 1995. (Cited on page 226.)Google Scholar
[974] D. E., Varberg. Convergence of quadratic forms in independent random variables. Annals of Mathematical Statistics, 37:567–576, 1966. (Cited on page 281.)Google Scholar
[975] J., Veenstra and A. I., McLeod. Hyperbolic decay time series models. In press, 2012. (Cited on page 572.)Google Scholar
[976] J. Q., Veenstra. Persistence and Anti-persistence: Theory and Software. Ph.D. thesis, Western University, 2012. (Cited on page 555.)
[977] M. S., Veillette and M. S., Taqqu. A technique for computing the PDFs and CDFs of nonnegative infinitely divisible random variables. Journal of Applied Probability, 48(1):217–237, 2011. (Cited on page 271.)Google Scholar
[978] M. S., Veillette and M. S., Taqqu. Berry-Esseen and Edgeworth approximations for the normalized tail of an infinite sum of independent weighted gamma random variables. Stochastic Processes and their Applications, 122(3):885–909, 2012. (Cited on page 271.)Google Scholar
[979] M. S., Veillette and M. S., Taqqu. Properties and numerical evaluation of the Rosenblatt distribution. Bernoulli, 19(3):982–1005, 2013. (Cited on pages 264, 265, 266, 267, 270, 271, 272, 280, and 281.)Google Scholar
[980] M. S., Veillette and M. S., Taqqu. Supplement to “Properties and numerical evaluation of the Rosenblatt distribution”. 2013. (Cited on pages 266, 271, 272, and 281.)
[981] D., Veitch and P., Abry. A wavelet-based joint estimator of the parameters of long-range dependence. IEEE Transactions on Information Theory, 45(3):878–897, 1999. (Cited on page 111.)Google Scholar
[982] D., Veitch, M. S., Taqqu, and P., Abry. On the automatic selection of the onset of scaling. Fractals, 11(4):377–390, 2003. (Cited on page 112.)Google Scholar
[983] D., Veitch, A. Gorst-Rasmussen, and A. Gefferth. Why FARIMA models are brittle. Fractals, 21(2):1350012, 12, 2013. (Cited on page 109.)Google Scholar
[984] C., Velasco. Gaussian semiparametric estimation of non-stationary time series. Journal of Time Series Analysis, 20(1):87–127, 1999. (Cited on page 572.)Google Scholar
[985] C., Velasco. Non-stationary log-periodogram regression. Journal of Econometrics, 91(2):325–371, 1999. (Cited on pages 111 and 573.)Google Scholar
[986] C., Velasco. Non-Gaussian log-periodogram regression. Econometric Theory, 16:44–79, 2000. (Citedonpage 111.)Google Scholar
[987] C., Velasco. Gaussian semi-parametric estimation of fractional cointegration. Journal of Time Series Analysis, 24(3):345–378, 2003. (Cited on page 536.)Google Scholar
[988] C., Velasco and P. M., Robinson. Whittle pseudo-maximum likelihood estimation for nonstationary time series. Journal of the American Statistical Association, 95(452):1229–1243, 2000. (Cited on pages 546 and 571.)Google Scholar
[989] S., Veres and M., Boda. The chaotic nature of TCP congestion control. In Proceedings of IEEE INFOCOM, volume 3, pages 1715–1723, 2000. (Cited on page 225.)Google Scholar
[990] W., Vervaat. Sample paths of self-similar processes with stationary increments. The Annals of Probability, 13:1–27, 1985. (Cited on pages 108 and 110.)Google Scholar
[991] W., Vervaat. Properties of general self-similar processes. Bulletin of the International Statistical Institute, 52(Book 4):199–216, 1987. (Cited on page 110.)Google Scholar
[992] B., Vollenbröker. Strictly stationary solutions of ARMA equations with fractional noise. Journal of Time Series Analysis, 33(4):570–582, 2012. (Cited on page 109.)Google Scholar
[993] S., Wainger. Special trigonometric series in k-dimensions. Memoirs of the American Mathematical Society, 59:102, 1965. (Cited on pages 526, 527, and 528.)Google Scholar
[994] L., Wang. Memory parameter estimation for long range dependent random fields. Statistics & Probability Letters, 79(21):2297–2306, 2009. (Cited on page 537.)Google Scholar
[995] W., Wang. Almost-sure path properties of fractional Brownian sheet. Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 43(5):619–631, 2007. (Cited on page 537.)Google Scholar
[996] Y., Wang. An invariance principle for fractional Brownian sheets. Journal of Theoretical Probability, 27(4):1124–1139, 2014. (Cited on page 537.)Google Scholar
[997] Z., Wang, L., Yan and X., Yu. Weak approximation of the fractional Brownian sheet from random walks. Electronic Communications in Probability, 18: no. 90, 13, 2013. (Cited on page 537.)Google Scholar
[998] L. M., Ward and P. E, Greenwood. 1/f noise. Scholarpedia, 2(12):1537, 2007. revision æ90924. (Cited on page 227.)Google Scholar
[999] G. N., Watson. A Treatise on the Theory of Bessel Functions. Cambridge Mathematical Library. Cambridge: Cambridge University Press, 1995. Reprint of the second (1944) edition. (Cited on page 458.)
[1000] K., Weierstrass. Über continuirliche Functionen eines reellen Arguments, die für keinen Werth des letzteren einen bestimmten Differentialquotienten besitzen. Presented at the Königlische Akademie der Wissenschaften in Berlin on 18 July 1872. Published in Volume 2 of his complete works, pages 71-74, see Weierstrass (1894-1927), 1872. (Cited on page 216.)
[1001] K., Weierstrass. Matematische Werke. Berlin and Leipzig: Mayer & Muller, 1894–1927. 7 volumes. (Cited on page 216.)
[1002] H. L., Weinert. Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing. Stroudsburg, PA: Hutchinson Ross, 1982. (Cited on page 384.)
[1003] H., Wendt, A., Scherrer, P., Abry and S., Achard. Testing fractal connectivity in multivariate long memory processes. In Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, pages 2913–2916. IEEE, 2009. (Cited on page 537.)
[1004] W., Werner. Random planar curves and Schramm-Loewner evolutions. In Lectures on probability theory and statistics, volume 1840 of Lecture Notes in Math., pages 107–195. Berlin: Springer, 2004. (Cited on page 227.)
[1005] P., Whittle. Hypothesis Testing in Time Series Analysis. New York: Hafner, 1951. (Cited on page 570.)
[1006] P., Whittle. The analysis of multiple stationary time series. Journal of the Royal Statistical Society. Series B. Methodological, 15:125–139, 1953. (Cited on page 570.)Google Scholar
[1007] P., Whittle. On the variation of yield variance with plot size. Biometrika, 43:337–343, 1956. (Cited on page 109.)Google Scholar
[1008] R. J., Hyndman with contributions from G., Athanasopoulos, S., Razbash, D., Schmidt, Z., Zhou, Y., Khan, and C., Bergmeir. forecast: Forecasting functions for time series and linear models, 2013. URL http://CRAN.R-project.org/package=forecast. R package version 4.8. (Cited on page 555.)
[1009] R. L., Wolpert and M. S., Taqqu. Fractional Ornstein–Uhlenbeck Lévy processes and the Telecom process: Upstairs and downstairs. Signal Processing, 85(8):1523–1545, 2005. (Cited on page 111.)Google Scholar
[1010] A. T. A., Wood and G., Chan. Simulation of stationary Gaussian processes in [0, 1] d. Journal of Computational and Graphical Statistics, 3(4):409–432, 1994. (Cited on page 112.)Google Scholar
[1011] G., Wornell. Signal Processing with Fractals: A Wavelet-Based Approach. Upper Saddle River, NJ: Prentice Hall PTR, 1996. (Cited on page 112.)
[1012] W. B., Wu. Empirical processes of long-memory sequences. Bernoulli, 9(5):809–831, 2003. (Cited on page 344.)Google Scholar
[1013] W. B., Wu and X., Shao. Invariance principles for fractionally integrated nonlinear processes. In Recent Developments in Nonparametric Inference and Probability, volume 50 of IMS Lecture Notes Monogr. Ser., pages 20–30. Beachwood, OH: Inst. Math. Statist., 2006. (Cited on page 611.)
[1014] W. B., Wu and X., Shao. A limit theorem for quadratic forms and its applications. Econometric Theory, 23(5):930–951, 2007. (Cited on page 571.)Google Scholar
[1015] W. B., Wu, Y., Huang and W., Zheng. Covariances estimation for long-memory processes. Advances in Applied Probability, 42(1): 137–157, 2010. (Cited on page 574.)Google Scholar
[1016] D., Wuertz, many others, and see the SOURCE file. fArma: ARMA Time Series Modelling, 2013. URL http://CRAN.R-project.org/package=fArma. R package version 3010.79. (Citedonpage 572.)
[1017] Y., Xiao. Sample path properties of anisotropic Gaussian random fields. In A minicourse on stochastic partial differential equations, volume 1962 of Lecture Notes in Math., pages 145–212. Berlin: Springer, 2009. (Cited on page 537.)
[1018] J., Xiong and X., Zhao. Nonlinear filtering with fractional Brownian motion noise. Stochastic Analysis and Applications, 23(1):55–67, 2005. (Cited on page 436.)Google Scholar
[1019] A. M., Yaglom. Correlation theory of processes with stationary random increments of order n. Matematicheski Sbornik, 37:141–196, 1955. English translation in American Mathematical Society Translations Series 2 8 (1958), 87-141. (Cited on page 110.)Google Scholar
[1020] A. M., Yaglom. Some classes of random fields in n-dimensional space, related to stationary random processes. Theory of Probability and its Applications, II (3):273–320, 1957. (Cited on pages 476, 514, and 530.)Google Scholar
[1021] A. M., Yaglom. Correlation Theory of Stationary and Related Random Functions. Volume I: Basic Results. Springer Series in Statistics. Springer, 1987. (Cited on pages 476 and 514.)
[1022] Y., Yajima. On estimation of long-memory time series models. Australian Journal of Statistics, 27 (3): 303–320, 1985. (Cited on page 570.)Google Scholar
[1023] C. Y., Yau and R. A., Davis. Likelihood inference for discriminating between long-memory and change-point models. Journal of Time Series Analysis, 33(4):649–664, 2012. (Cited on page 225.)Google Scholar
[1024] L. C., Young. An inequality of the Hölder type, connected with Stieltjes integration. Acta Mathematica, 67(1):251–282, 1936. (Cited on page 408.)Google Scholar
[1025] P., Zaffaroni. Contemporaneous aggregation of linear dynamic models in large economies. Journal of Econometrics, 120(1):75–102, 2004. (Cited on page 223.)Google Scholar
[1026] P., Zaffaroni. Aggregation and memory of models of changing volatility. Journal of Econometrics, 136(1):237–249, 2007. ISSN 0304-4076. (Cited on page 223.)Google Scholar
[1027] M., Zähle. Integration with respect to fractal functions and stochastic calculus. I. Probability Theory and Related Fields, 111(3):333–374, 1998. (Cited on page 435.)Google Scholar
[1028] T., Zhang, H.-C., Ho, M., Wendler, and W. B., Wu. Block sampling under strong dependence. Stochastic Processes and their Applications, 123(6):2323–2339, 2013. (Cited on page 574.)Google Scholar
[1029] V. M., Zolotarev. One-dimensional Stable Distributions, volume 65 of “Translations of mathematical monographs”. American Mathematical Society, 1986. Translation from the original 1983 Russian edition. (Cited on pages 111 and 585.)
[1030] A., Zygmund. Trigonometric Series. 2nd ed. Vols. I, II. New York: Cambridge University Press, 1959. (Cited on pages 291, 353, and 575.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Bibliography
  • Vladas Pipiras, University of North Carolina, Chapel Hill, Murad S. Taqqu, Boston University
  • Book: Long-Range Dependence and Self-Similarity
  • Online publication: 11 May 2017
  • Chapter DOI: https://doi.org/10.1017/CBO9781139600347.017
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Bibliography
  • Vladas Pipiras, University of North Carolina, Chapel Hill, Murad S. Taqqu, Boston University
  • Book: Long-Range Dependence and Self-Similarity
  • Online publication: 11 May 2017
  • Chapter DOI: https://doi.org/10.1017/CBO9781139600347.017
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bibliography
  • Vladas Pipiras, University of North Carolina, Chapel Hill, Murad S. Taqqu, Boston University
  • Book: Long-Range Dependence and Self-Similarity
  • Online publication: 11 May 2017
  • Chapter DOI: https://doi.org/10.1017/CBO9781139600347.017
Available formats
×