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Limit theorems for renewal processes with infinite mean interarrival time under random inspection

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  • Rauwolf, Diana

Abstract

Analogues to fundamental asymptotic relations in renewal theory are considered under the assumption that the time is a random variable and that the interarrival times have infinite mean. Limits are given for interarrival times with regularly varying tail and for sequences of parameters of the respective random-time distribution under mild conditions. An application to alternating renewal processes is shown.

Suggested Citation

  • Rauwolf, Diana, 2026. "Limit theorems for renewal processes with infinite mean interarrival time under random inspection," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001725
    DOI: 10.1016/j.spl.2025.110527
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    References listed on IDEAS

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    1. Angus, John & Ding, Yujia, 2020. "On the ratio of current age to total life for null recurrent renewal processes," Statistics & Probability Letters, Elsevier, vol. 162(C).
    2. Diana Rauwolf & Udo Kamps, 2023. "Quantifying the Inspection Paradox with Random Time," The American Statistician, Taylor & Francis Journals, vol. 77(3), pages 274-282, July.
    3. Piaomu Liu & Edsel A. Peña, 2016. "Sojourning With the Homogeneous Poisson Process," The American Statistician, Taylor & Francis Journals, vol. 70(4), pages 413-423, October.
    4. Kamps, Udo & Rauwolf, Diana, 2023. "A record-values property of a renewal process with random inspection time," Statistics & Probability Letters, Elsevier, vol. 195(C).
    5. Salehi, E.T. & Badía, F.G. & Asadi, M., 2012. "Preservation properties of a homogeneous Poisson process stopped at an independent random time," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 574-585.
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