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A refinement of the coupling method in renewal theory

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  • Ney, Peter

Abstract

An overjump Markov chain associated with a pair of random walks is used to obtain a sharp estimate of their coupling time; and thence of the convergence rate of a renewal process. Lattice valued and non-singular cases are treated.

Suggested Citation

  • Ney, Peter, 1981. "A refinement of the coupling method in renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 11(1), pages 11-26, March.
    • Handle: RePEc:eee:spapps:v:11:y:1981:i:1:p:11-26
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    Cited by:

    1. Vitaliy Golomoziy & Yuliya Mishura, 2020. "Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    2. Geluk, J.L. & Frenk, J.B.G., 2011. "Renewal theory for random variables with a heavy tailed distribution and finite variance," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 77-82, January.
    3. Mitov, Kosto V. & Omey, Edward, 2014. "Intuitive approximations for the renewal function," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 72-80.
    4. Omey, Edward & Van Gulck, Stefan, 2015. "Intuitive approximations in discrete renewal theory, Part 1: Regularly varying case," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 68-74.

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