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Generalizations of the arithmetic case of Blackwell’s renewal theorem

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  • Hadjicostas, Petros

Abstract

Using elementary techniques, for discrete-time renewal processes, we provide asymptotic results for the probability of renewal at time n using the binomial moments of the underlying discrete distribution. Using these results, we also provide an alternative derivation of the asymptotics for the first two moments of the number of renewals up to time n.

Suggested Citation

  • Hadjicostas, Petros, 2019. "Generalizations of the arithmetic case of Blackwell’s renewal theorem," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 124-131.
    • Handle: RePEc:eee:stapro:v:149:y:2019:i:c:p:124-131
    DOI: 10.1016/j.spl.2019.01.031
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    References listed on IDEAS

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    1. Chaudhry, Mohan & Fisher, Brent, 2013. "Simple and elegant derivations for some asymptotic results in the discrete-time renewal process," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 315-319.
    2. 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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