Random walk in random environment with asymptotically zero perturbation

Mikhail V. Menshikov, Andrew Wade

Research output: Contribution to journalArticle

5 Citations (Scopus)
31 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

Keywords

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

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