Logarithmic speeds for one-dimensional perturbed random walks in random environments

MV Menshikov, AR Wade

Research output: Contribution to journalArticle (Academic Journal)

6 Citations (Scopus)

Abstract

We study the random walk in a random environment on , where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) a random walk in a random environment perturbed from Sinai's regime; (ii) a simple random walk with a random perturbation. We give almost sure results on how far the random walker is from the origin, for almost every environment. We give both upper and lower almost sure bounds. These bounds are of order (logt)[beta], for [beta][set membership, variant](1,[infinity]), depending on the perturbation. In addition, in the ergodic cases, we give results on the rate of decay of the stationary distribution.
Translated title of the contributionLogarithmic speeds for one-dimensional perturbed random walks in random environments
Original languageEnglish
Pages (from-to)389 - 416
Number of pages28
JournalStochastic Processes and their Applications
Volume113 (3)
DOIs
Publication statusPublished - Mar 2008

Bibliographical note

Publisher: Elsevier

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