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Via a coupling argument, it is proved that the solution to a renewal equation has a power law decay rate in the case of a spread out interarrival distribution. By the regenerative property, the convergence in distribution for the recurrence times of the renewal process is established as well as that of the compensator of the renewal counting process. All results are proved under mild assumptions of existence of moments.

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Results for Convergence Rates Associated with Renewal Processes

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  • 发表日期：

    2025年

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  • Luis Iván Hernández Ruíz

摘要

Via a coupling argument, it is proved that the solution to a renewal equation has a power law decay rate in the case of a spread out interarrival distribution. By the regenerative property, the convergence in distribution for the recurrence times of the renewal process is established as well as that of the compensator of the renewal counting process. All results are proved under mild assumptions of existence of moments.