This article is cited in 2 papers

On transience conditions for Markov chains and random walks

D. É. Denisov^a, S. G. Foss<sup>ba

a</sup> Heriot Watt University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

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.

Keywords: Markov chain, martingale, transience, uniform integrability, test function, random walk.

UDC: 519.21

Received: 15.08.2001

 English version: Siberian Mathematical Journal, 2003, 44:1, 44–57

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