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Random walk in random environment with asymptotically zero perturbation

Menshikov, M.V.; Wade, A.R.

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Abstract

We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on $\Z^+=\{0,1,2,\ldots\}$, with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results complement existing criteria for random walks in random environments and for Markov chains with asymptotically zero drift, and are significantly different to these previously studied cases. Our method is based on a martingale technique - the method of Lyapunov functions.

Citation

Menshikov, M., & Wade, A. (2006). Random walk in random environment with asymptotically zero perturbation. Journal of the European Mathematical Society, 8(3), 491-513. https://doi.org/10.4171/jems/64

Journal Article Type Article
Publication Date 2006
Deposit Date Jan 9, 2009
Publicly Available Date Mar 28, 2024
Journal Journal of the European Mathematical Society
Print ISSN 1435-9855
Electronic ISSN 1435-9863
Publisher EMS Press
Peer Reviewed Peer Reviewed
Volume 8
Issue 3
Pages 491-513
DOI https://doi.org/10.4171/jems/64
Keywords Random walk in random environment, Perturbation of Sinai's regime, Recurrence/transience criteria, Lyapunov functions.

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