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Random walk in random environment with asymptotically zero perturbation

Menshikov, Mikhail V. and Wade, Andrew (2006) Random walk in random environment with asymptotically zero perturbation. Journal of the European Mathematical Society, 8 (3). pp. 491-513. ISSN 1435-9855

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    Abstract

    We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on \Z+={0,1,2,…}, 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.

    Item type: Article
    ID code: 34459
    Keywords: random walk in random environment, perturbation of Sinai's regime, recurrence/transience criteria, Lyapunov functions, Probabilities. Mathematical statistics
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 04 Nov 2011 12:52
    Last modified: 20 Jul 2013 21:36
    URI: http://strathprints.strath.ac.uk/id/eprint/34459

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