Siberian Mathematical Journal

, Volume 44, Issue 1, pp 44–57 | Cite as

On Transience Conditions for Markov Chains and Random Walks

  • D. E. Denisov
  • S. G. Foss
Article
  • 40 Downloads

Abstract

We prove a new transience criterion for Markov chains on an arbitrary state space and give a corollary for real-valued chains. We show by example that in the case of a homogeneous random walk with infinite mean the proposed sufficient conditions are close to those necessary. We give a new proof of the well-known criterion for finiteness of the supremum of a random walk.

Markov chain martingale transience uniform integrability test function random walk 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • D. E. Denisov
    • 1
  • S. G. Foss
    • 2
  1. 1.Heriot-Watt UniversityEdinburgh
  2. 2.Sobolev Institute of Mathematics, NovosibirskHeriot-Watt UniversityEdinburgh

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