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Convolutions of Long-Tailed and Subexponential Distributions

Part of: Stochastic processes Limit theorems Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Sergey Foss ,
Dmitry Korshunov  and
Stan Zachary
Sergey Foss*
Affiliation:
Heriot-Watt University and Sobolev Institute of Mathematics
Dmitry Korshunov*
Affiliation:
Sobolev Institute of Mathematics
Stan Zachary*
Affiliation:
Heriot-Watt University
*
∗Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK.
∗∗∗Postal address: Sobolev Institute of Mathematics, Academic Koptyug Propekt 4, Novosibirsk, 630090, Russia. Email address: korshunov@math.nsc.ru
∗Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK.
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Abstract

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Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and also showing that the standard properties of such convolutions follow as easy consequences.

Keywords

Long-tailed distributionsubexponential distribution

MSC classification

Secondary: 60E05: Distributions 60F10: Large deviations 60G70: Extreme value theory; extremal processes
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 3 , September 2009 , pp. 756 - 767
Copyright
Copyright © Applied Probability Trust 2009 

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