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On Transience Conditions for Markov Chains and Random Walks

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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.

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Authors and Affiliations

  1. Heriot-Watt University, Edinburgh

    D. E. Denisov

  2. Sobolev Institute of Mathematics, Novosibirsk, Heriot-Watt University, Edinburgh

    S. G. Foss

Authors
  1. D. E. Denisov
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  2. S. G. Foss
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Denisov, D.E., Foss, S.G. On Transience Conditions for Markov Chains and Random Walks. Siberian Mathematical Journal 44, 44–57 (2003). https://doi.org/10.1023/A:1022008203109

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  • DOI: https://doi.org/10.1023/A:1022008203109

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