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

Menshikov, Mikhail V. and Wade, Andrew R. (2008) Logarithmic speeds for one-dimensional perturbed random walk in random environment. Stochastic Processes and their Applications, 118 (3). pp. 389-416. ISSN 0304-4149

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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.

Item type: Article
ID code: 13395
Keywords: random walk, random environment, logarithmic speeds, almost sure behaviour, slow transience, Probabilities. Mathematical statistics, Mathematics, Modelling and Simulation, Applied Mathematics, Statistics and Probability
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Mrs Carolynne Westwood
Date Deposited: 12 Nov 2009 13:50
Last modified: 15 Apr 2015 10:18
URI: http://strathprints.strath.ac.uk/id/eprint/13395

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