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Extremal properties of shot noise processes

Published online by Cambridge University Press:  01 July 2016

Tailen Hsing  and
J. L. Teugels
Tailen Hsing*
Affiliation:
Texas A&M University
J. L. Teugels*
Affiliation:
Katholieke University Leuven
*
∗Postal address: Department of Statistics, Texas A&M University, College Station, TX 77843–3143, USA.
∗∗Postal address: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3030 Heverlee, Belgium.
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Abstract

Consider the shot noise process X(t):= Σih(t – τi), , where h is a bounded positive non-increasing function supported on a finite interval, and the are the points of a renewal process η on [0, ). In this paper, the extremal properties of {X(t)} are studied. It is shown that these properties can be investigated in a natural way through a discrete-time process which records the states of {X(t)} at the points of η. The important special case where η is Poisson is treated in detail, and a domain-of-attraction result for the compound Poisson distribution is obtained as a by-product.

Keywords

EXTREME VALUEPOINT PROCESSRENEWAL PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 513 - 525
Copyright
Copyright © Applied Probability Trust 1989 

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