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Nonexponential asymptotics for the solutions of renewal equations, with applications

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Chuancun Yin  and
Junsheng Zhao
Chuancun Yin*
Affiliation:
Qufu Normal University
Junsheng Zhao*
Affiliation:
Qufu Normal University
*
∗Postal address: Department of Mathematics, Qufu Normal University, Qufu, 273165, Shandong, P. R. China.
∗Postal address: Department of Mathematics, Qufu Normal University, Qufu, 273165, Shandong, P. R. China.
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Abstract

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Nonexponential asymptotics for solutions of two specific defective renewal equations are obtained. These include the special cases of asymptotics for a compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the asymptotic behavior of the demographic birth rate of females, the perpetual put option in mathematics of finance, and the renewal function for terminating renewal processes.

Keywords

Asymptoticsdefective renewal equationdeterministic population modelcompound geometric distributionheavy-tailed distributionperpetual put optionrenewal function

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60K10: Applications (reliability, demand theory, etc.) 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 815 - 824
Copyright
© Applied Probability Trust 2006 

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