JournalsjemsVol. 8, No. 3pp. 491–513

Random walk in random environment with asymptotically zero perturbation

  • M.V. Menshikov

    University of Durham, United Kingdom
  • Andrew R. Wade

    University of Bath, United Kingdom
Random walk in random environment with asymptotically zero perturbation cover
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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,}\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.

Cite this article

M.V. Menshikov, Andrew R. Wade, Random walk in random environment with asymptotically zero perturbation. J. Eur. Math. Soc. 8 (2006), no. 3, pp. 491–513

DOI 10.4171/JEMS/64