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The Key Renewal Theorem for a Transient Markov Chain

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  • Dmitry Korshunov

    (Sobolev Institute of Mathematics and Novosibirsk State University)

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.

Suggested Citation

  • Dmitry Korshunov, 2008. "The Key Renewal Theorem for a Transient Markov Chain," Journal of Theoretical Probability, Springer, vol. 21(1), pages 234-245, March.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:1:d:10.1007_s10959-007-0132-8
    DOI: 10.1007/s10959-007-0132-8
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    References listed on IDEAS

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    1. Alsmeyer, Gerold, 1994. "On the Markov renewal theorem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 37-56, March.
    2. Makoto Maejima, 1975. "On local limit theorems and Blackwell's renewal theorem for independent random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 507-520, December.
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    Cited by:

    1. Palle Jorgensen & Feng Tian, 2019. "Realizations and Factorizations of Positive Definite Kernels," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1925-1942, December.

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