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Random walk in random environment with asymptotically zero perturbation.

Menshikov, M. V. and Wade, A. R. (2006) 'Random walk in random environment with asymptotically zero perturbation.', Journal of the European Mathematical Society., 8 (3). pp. 491-513.

Abstract

We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on $\Z^+=\{0,1,2,\ldots\}$, 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
Keywords:Random walk in random environment, Perturbation of Sinai's regime, Recurrence/transience criteria, Lyapunov functions.
Full text:PDF - Published Version (196Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.4171/JEMS/64
Record Created:09 Jan 2009
Last Modified:01 Feb 2013 14:54

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