Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T09:10:32.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Prediction of shot noise

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Robert B. Lund ,
Ronald W. Butler  and
Robert L. Paige
Robert B. Lund*
Affiliation:
University of Georgia
Ronald W. Butler*
Affiliation:
Colorado State University
Robert L. Paige*
Affiliation:
Colorado State University
*
∗Postal address: Department of Statistics, The University of Georgia, Athens, GA 30602–1952. Email address: [email protected]
∗∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523.
∗∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523.
Get access Rights & Permissions [Opens in a new window]

Abstract

Prediction of future values of a shot noise process observed on a discrete lattice of points is considered. The shot magnitudes are assumed to be independent and identically distributed and to arrive via a Poisson process; the effect of each shot dissipates and/or accumulates according to a known shot function. Conditional mean and linear point predictors of future process values are developed. Distributional prediction, obtained through saddlepoint approximation of the conditional distributions of the process, is also explored.

Keywords

Predictionshot noisemean squared errorsaddlepoint approximation

MSC classification

Primary: 60G25: Prediction theory
Secondary: 60G20: Generalized stochastic processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 374 - 388
Copyright
Copyright © Applied Probability Trust 1999 

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

Barndorff-Nielsen, O. E., and Cox, D. R. (1979). Edgeworth and saddlepoint approximations with statistical applications (with Discussion). J. R. Statist. Soc. B 41, 279–312.Google Scholar
Bevan, S., Kullberg, R., and Rice, J. (1979). An analysis of membrane noise. Ann. Statist. 7, 237–257.CrossRefGoogle Scholar
Brockwell, P. J., and Davis, R. A. (1991). Time Series: Theory and Methods, 2nd edn. Springer, New York.CrossRefGoogle Scholar
Cox, D. R., and Isham, V. (1980). Point Processes. Chapman and Hall, London.Google Scholar
Daniels, H. (1987). Tail probability approximations. Int. Statist. Rev. 55, 37–48.CrossRefGoogle Scholar
Helstrom, C. W., and Ho, C. L. (1992). Analysis of avalanche diode receivers by saddlepoint integration. IEEE Trans. Commun. 40, 1327–1328.CrossRefGoogle Scholar
Lauger, P. (1975). Shot noise in ion channels. Biochem. Biophys. Acta. 413, 1–10.CrossRefGoogle ScholarPubMed
Lugannani, R., and Rice, S. O. (1980). Saddlepoint approximations for the distribution of the sum of independent random variables. Adv. Appl. Prob. 12, 475–490.CrossRefGoogle Scholar
Lund, R. B. (1996). The stability of storage models with shot noise input. J. Appl. Prob. 33, 830–839.CrossRefGoogle Scholar
Marcus, A. (1975). Some exact distributions in traffic noise theory. Adv. Appl. Prob. 7, 593–606.CrossRefGoogle Scholar
Rice, J. (1977). On generalized shot noise. Adv. Appl. Prob. 9, 553–565.CrossRefGoogle Scholar
Skovgaard, I. M. (1987). Saddlepoint expansions for conditional distributions. J. Appl. Prob. 24, 875–887.CrossRefGoogle Scholar
Snyder, Donald L., (1975). Random Point Processes. Wiley, New York.Google Scholar
Temme, N. M. (1982). The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions. SIAM J. Math. Anal. 13, 239–253.CrossRefGoogle Scholar