Random walk in random environment with asymptotically zero perturbation

Mikhail V. Menshikov, Andrew Wade

Research output: Contribution to journalArticle

5 Citations (Scopus)
27 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)491-513
Number of pages23
JournalJournal of the European Mathematical Society
Volume8
Issue number3
DOIs
Publication statusPublished - Sep 2006

Fingerprint

Random Walk in Random Environment
Lyapunov functions
Markov processes
Perturbation
Transience
Random Environment
Zero
Ergodicity
Martingale
Recurrence
Lyapunov Function
Null
Markov chain
Complement

Keywords

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

Cite this

Menshikov, Mikhail V. ; Wade, Andrew. / Random walk in random environment with asymptotically zero perturbation. In: Journal of the European Mathematical Society. 2006 ; Vol. 8, No. 3. pp. 491-513.
@article{7c79363919f943b68ce4428f4820e5f6,
title = "Random walk in random environment with asymptotically zero perturbation",
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.",
keywords = "random walk in random environment, perturbation of Sinai's regime, recurrence/transience criteria, Lyapunov functions",
author = "Menshikov, {Mikhail V.} and Andrew Wade",
year = "2006",
month = "9",
doi = "10.4171/JEMS/64",
language = "English",
volume = "8",
pages = "491--513",
journal = "Journal of the European Mathematical Society",
issn = "1435-9855",
number = "3",

}

Random walk in random environment with asymptotically zero perturbation. / Menshikov, Mikhail V.; Wade, Andrew.

In: Journal of the European Mathematical Society, Vol. 8, No. 3, 09.2006, p. 491-513.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Random walk in random environment with asymptotically zero perturbation

AU - Menshikov, Mikhail V.

AU - Wade, Andrew

PY - 2006/9

Y1 - 2006/9

N2 - 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.

AB - 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.

KW - random walk in random environment

KW - perturbation of Sinai's regime

KW - recurrence/transience criteria

KW - Lyapunov functions

UR - http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=8&iss=3&rank=4

U2 - 10.4171/JEMS/64

DO - 10.4171/JEMS/64

M3 - Article

VL - 8

SP - 491

EP - 513

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

SN - 1435-9855

IS - 3

ER -