Asymptotics for solutions of a defective renewal equation with applications

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.

Keywords

Asymptotics / defective renewal equation / Gerber-Shiu discounted penalty function / heavy-tailed distribution / ruin theory / subexponential density / reliability theory

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