Random walk in random environment with asymptotically zero perturbation

MV Menshikov, AR Wade

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)

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.
Translated title of the contributionRandom walk in random environment with asymptotically zero perturbation
Original languageEnglish
Pages (from-to)491 - 513
Number of pages23
JournalJournal of the European Mathematical Society
Volume8 (3)
Publication statusPublished - Sep 2006

Bibliographical note

Publisher: European Mathematical Society

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