Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T17:33:05.009Z Has data issue: false hasContentIssue false
  • English
  • Français

A Symmetry Property for a Class of Random Walks in Stationary Random Environments on Z

Part of: Special processes Markov processes

Published online by Cambridge University Press:  04 February 2016

Jean-Marc Derrien  and
Frédérique Plantevin
Jean-Marc Derrien*
Affiliation:
Université de Brest
Frédérique Plantevin*
Affiliation:
Université de Brest
*
∗ Postal address: Département de Mathématiques, Université de Brest, UEB - 6, Avenue Victor Le Gorgeu, CS 93837, 29238 Brest Cedex 3, France.
∗ Postal address: Département de Mathématiques, Université de Brest, UEB - 6, Avenue Victor Le Gorgeu, CS 93837, 29238 Brest Cedex 3, France.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A correspondence formula between the laws of dual Markov chains on Z with two transition jumps is established. This formula contributes to the study of random walks in stationary random environments. Counterexamples with more than two jumps are exhibited.

Keywords

Markov chaindualityrandom walkstationary random environmentconductance and resistance

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K37: Processes in random environments
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 338 - 350
Copyright
© Applied Probability Trust 

References

De Masi, A., Ferrari, P. A., Goldstein, S. and Wick, W. D. (1989). An invariance principle for reversible Markov processes. Applications to random motions in random environments. J. Statist. Phys. 55, 787–855.CrossRefGoogle Scholar
Depauw, J. and Derrien, J.-M. (2009). Variance limite d'une marche aléatoire réversible en milieu aléatoire sur {Z}. C. R. Acad. Sci. Paris 347, 401–406.CrossRefGoogle Scholar
Derriennic, Y. (1999). Random walks with Jumps in random environments (examples of cycle and weight representations). In Probability Theory and Mathematical Statistics (Proc. 7th Internat. Vilnius Conf., August 1998), eds Grigelionis, B. et al., pp. 199–212.Google Scholar
Derriennic, Y. (1999). Sur la récurrence des marches aléatoires unidimensionnelles en environnement aléatoire. C. R. Acad. Sci. Paris 329, 65–70.CrossRefGoogle Scholar
Dette, H., Fill, J. A., Pitman, J. and Studden, W. J. (1997). Wall and Siegmund duality relations for birth and death chains with reflecting barrier. J. Theoret. Prob. 10, 349–374.CrossRefGoogle Scholar
Kozlov, S. M. (1985). The method of averaging and walks in inhomogeneous environments. Russian Math. Surveys 40, 73–145.CrossRefGoogle Scholar
Petersen, K. (1983). Ergodic Theory (Camb. Stud. Adv. Math. 2). Cambridge University Press.CrossRefGoogle Scholar