Random walk in random environment with asymptotically zero perturbation

Menshikov, 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 -