# Random walk in random environment with asymptotically zero perturbation

M.V. Menshikov; Andrew R. Wade

Journal of the European Mathematical Society (2006)

- Volume: 008, Issue: 3, page 491-513
- ISSN: 1435-9855

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topMenshikov, M.V., and Wade, Andrew R.. "Random walk in random environment with asymptotically zero perturbation." Journal of the European Mathematical Society 008.3 (2006): 491-513. <http://eudml.org/doc/277378>.

@article{Menshikov2006,

abstract = {We give criteria for ergodicity, transience and null-recurrence for the random walk in random environment on $\mathbb \{Z\}^+=\lbrace 0,1,2,\dots \rbrace $, 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 from the previously studied cases. Our method is based on a martingale
technique—the method of Lyapunov functions.},

author = {Menshikov, M.V., Wade, Andrew R.},

journal = {Journal of the European Mathematical Society},

keywords = {random walk in random environment; perturbation of Sinai's regime; recurrence/transience criteria; Lyapunov functions; random walk in random environment; perturbation of Sinai's regime; recurrence/transience criteria; Lyapunov functions},

language = {eng},

number = {3},

pages = {491-513},

publisher = {European Mathematical Society Publishing House},

title = {Random walk in random environment with asymptotically zero perturbation},

url = {http://eudml.org/doc/277378},

volume = {008},

year = {2006},

}

TY - JOUR

AU - Menshikov, M.V.

AU - Wade, Andrew R.

TI - Random walk in random environment with asymptotically zero perturbation

JO - Journal of the European Mathematical Society

PY - 2006

PB - European Mathematical Society Publishing House

VL - 008

IS - 3

SP - 491

EP - 513

AB - We give criteria for ergodicity, transience and null-recurrence for the random walk in random environment on $\mathbb {Z}^+=\lbrace 0,1,2,\dots \rbrace $, 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 from the previously studied cases. Our method is based on a martingale
technique—the method of Lyapunov functions.

LA - eng

KW - random walk in random environment; perturbation of Sinai's regime; recurrence/transience criteria; Lyapunov functions; random walk in random environment; perturbation of Sinai's regime; recurrence/transience criteria; Lyapunov functions

UR - http://eudml.org/doc/277378

ER -

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