Asymptotics for solutions of a defective renewal equation with applications

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  • School of Mathematical Sciences, Qufu Normal University;

Published date: 05 Sep 2008

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.

Cite this article

YIN Chuancun, ZHAO Xianghua . Asymptotics for solutions of a defective renewal equation with applications[J]. Frontiers of Mathematics in China, 2008 , 3(3) : 443 -459 . DOI: 10.1007/s11464-008-0024-y

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