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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
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 12 Nov 2009 13:50
      Last modified: 20 Jul 2013 21:54
      URI: http://strathprints.strath.ac.uk/id/eprint/13395

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