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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.
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Abstract

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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

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