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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, Applied Mathematics, Mathematics(all)
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date Deposited: 04 Nov 2011 12:52
Last modified: 15 Apr 2015 10:59
Related URLs:
URI: http://strathprints.strath.ac.uk/id/eprint/34459

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