Journal of Applied Probability

A symmetry property for a class of random walks in stationary random environments on Z

Jean-Marc Derrien and Frédérique Plantevin

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

J. Appl. Probab., Volume 49, Number 2 (2012), 338-350.

First available in Project Euclid: 16 June 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K37: Processes in random environments

Markov chain duality random walk stationary random environment conductance and resistance


Derrien, Jean-Marc; Plantevin, Frédérique. A symmetry property for a class of random walks in stationary random environments on Z. J. Appl. Probab. 49 (2012), no. 2, 338--350. doi:10.1239/jap/1339878790.

Export citation


  • 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.
  • 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.
  • 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 B. Grigelionis et al., pp. 199–212.
  • Derriennic, Y. (1999). Sur la récurrence des marches aléatoires unidimensionnelles en environnement aléatoire. C. R. Acad. Sci. Paris 329, 65–70.
  • 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.
  • Kozlov, S. M. (1985). The method of averaging and walks in inhomogeneous environments. Russian Math. Surveys 40, 73–145.
  • Petersen, K. (1983). Ergodic Theory (Camb. Stud. Adv. Math. 2). Cambridge University Press.