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The Key Renewal Theorem for a Transient Markov Chain

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Abstract

We consider a time-homogeneous real-valued Markov chain X n , n≥0. Suppose that this chain is transient, that is, X n generates a σ-finite renewal measure. We prove the key renewal theorem under the condition that this chain has jumps that are asymptotically homogeneous at infinity and asymptotically positive drift.

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  1. Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, 630090, Russia

    Dmitry Korshunov

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  1. Dmitry Korshunov
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Correspondence to Dmitry Korshunov.

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Korshunov, D. The Key Renewal Theorem for a Transient Markov Chain. J Theor Probab 21, 234–245 (2008). https://doi.org/10.1007/s10959-007-0132-8

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  • DOI: https://doi.org/10.1007/s10959-007-0132-8

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