Logarithmic speeds for one-dimensional perturbed random walk in random environment

M. V. Menshikov, Andrew R. Wade

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We study the random walk in random environment on Z+ = f0; 1; 2; : : :g, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) random walk in random environment perturbed from Sinai's regime; (ii) simple random walk with 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 (log t), for 2 (1;1), depending on the perturbation. In addition, in the ergodic cases, we give results on the rate of decay of the stationary distribution.
LanguageEnglish
Pages389-416
Number of pages28
JournalStochastic Processes and their Applications
Volume118
Issue number3
DOIs
Publication statusPublished - Mar 2008

Fingerprint

Random Walk in Random Environment
Random Perturbation
Logarithmic
Simple Random Walk
Stationary Distribution
Decay
Perturbation

Keywords

  • random walk
  • random environment
  • logarithmic speeds
  • almost sure behaviour
  • slow transience

Cite this

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Logarithmic speeds for one-dimensional perturbed random walk in random environment. / Menshikov, M. V.; Wade, Andrew R.

In: Stochastic Processes and their Applications, Vol. 118, No. 3, 03.2008, p. 389-416.

Research output: Contribution to journalArticle

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AU - Menshikov, M. V.

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AB - We study the random walk in random environment on Z+ = f0; 1; 2; : : :g, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) random walk in random environment perturbed from Sinai's regime; (ii) simple random walk with 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 (log t), for 2 (1;1), depending on the perturbation. In addition, in the ergodic cases, we give results on the rate of decay of the stationary distribution.

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KW - random environment

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KW - slow transience

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