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Asymptotics for solutions of a defective renewal equation with applications

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Abstract

In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Chuancun Yin & Xianghua Zhao

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  1. Chuancun Yin
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  2. Xianghua Zhao
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Correspondence to Chuancun Yin.

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Yin, C., Zhao, X. Asymptotics for solutions of a defective renewal equation with applications. Front. Math. China 3, 443–459 (2008). https://doi.org/10.1007/s11464-008-0024-y

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  • DOI: https://doi.org/10.1007/s11464-008-0024-y

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