Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T02:30:13.120Z Has data issue: false hasContentIssue false
  • English
  • Français

Large deviations for a Markov chain in a random landscape

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Nadine Guillotin-Plantard
Nadine Guillotin-Plantard*
Affiliation:
Université Claude Bernard Lyon 1
*
∗ Postal address: Université Claude Bernard Lyon 1, LaPCS, 50 avenue Tony Garnier, Domaine de Gerland, 69366 Lyon Cedex 07, France. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Let (Sk)k≥0 be a Markov chain with state space E and (ξx)x∊E be a family of ℝp-valued random vectors assumed independent of the Markov chain. The ξx could be assumed independent and identically distributed or could be Gaussian with reasonable correlations. We study the large deviations of the sum

Keywords

Markov chainrandom walkrandom scenerylocal timelarge deviations principlemoderate deviations principle

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 2 , June 2002 , pp. 375 - 393
Copyright
Copyright © Applied Probability Trust 2002 

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

Bolthausen, E. (1989). A central limit theorem for two-dimensional random walks in random sceneries. Ann. Prob. 17, 108–115.Google Scholar
Cabus, P. and Guillotin-Plantard, N. (2002). Functional limit theorems for U-statistics indexed by a random walk. Preprint. To appear in Stoch. Process. Appl. Google Scholar
Castell, F. and Pradeilles, F. (2001). Annealed large deviations for diffusions in a random Gaussian shear flow drift. To appear in Stoch. Process. Appl. 94, 171–197.Google Scholar
Csáki, E., König, W. and Shi, Z. (1999). An embedding for the Kesten–Spitzer random walk in random scenery. Stoch. Process. Appl. 82, 283–292.Google Scholar
Dembo, A., Peres, Y., Rosen, J. and Zeitouni, O. (2001). Thick points for planar Brownian motion and the Erdős–Taylor conjecture on random walk. Acta Math. 186, 239–270.Google Scholar
Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications. Springer, Berlin.Google Scholar
Erdős, P. and Taylor, S. J. (1960). Some problems concerning the structure of random walk paths. Acta Sci. Hungar. 11, 137–162.Google Scholar
Feller, W. (1971). An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. John Wiley, New York.Google Scholar
Guillotin, N. (1999). Edges occupation measure of a reversible Markov chain. Electron. Commun. Prob. 4, 87–90.Google Scholar
Kesten, H. and Spitzer, F. (1979). A limit theorem related to a new class of self-similar processes. Z. Wahrscheinlichkeitsth. 50, 5–25.Google Scholar
Khoshnevisan, D. and Lewis, T. M. (1998). A law of the iterated logarithm for stable processes in random scenery. Stoch. Process. Appl. 74, 89–121.Google Scholar
Kingman, J. F. C. (1968). The ergodic theory of subadditive stochastic processes. J. R. Statist. Soc. B 30, 499–510.Google Scholar
Lewis, T. M. (1992). A self-normalized law of the iterated logarithm for random walk in random scenery. J. Theoret. Prob. 5, 629–659.Google Scholar
Lewis, T. M. (1993). A law of the iterated logarithm for random walk in random scenery with deterministic normalizers. J. Theoret. Prob. 6, 209–230.Google Scholar
Petrov, V. V. (1995). Limit Theorems of Probability Theory, Sequences of Independent Random Variables. Oxford University Press.Google Scholar
Révész, P. and Shi, Z. (2000). Strong approximation of spatial random walk in random scenery. Stoch. Process. Appl. 88, 329–345.Google Scholar
Spitzer, F. L. (1976). Principles of Random Walks, 2nd edn. Springer, New York.Google Scholar
Worms, J. (2000). Principes de déviations modérées pour des martingales et applications statistiques. , Université de Marne-la-Vallée.Google Scholar