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Weak limit results for the extremes of a class of shot noise processes

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Patrick Homble  and
William P. McCormick
Patrick Homble*
Affiliation:
University of Georgia
William P. McCormick*
Affiliation:
University of Georgia
*
∗Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.
∗Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.
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Abstract

Shot noise processes form an important class of stochastic processes modeling phenomena which occur as shocks to a system and with effects that diminish over time. In this paper we present extreme value results for two cases — a homogeneous Poisson process of shocks and a non-homogeneous Poisson process with periodic intensity function. Shocks occur with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This work continues work of Hsing and Teugels (1989) and Doney and O'Brien (1991) to the case of random amplitudes.

Keywords

SHOT NOISEEXTREME VALUESSADDLEPOINT APPROXIMATION

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F05: Central limit and other weak theorems 60G99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 707 - 726
Copyright
Copyright © Applied Probability Trust 1995 

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