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Extremes for shot noise processes with heavy tailed amplitudes

Published online by Cambridge University Press:  14 July 2016

William P. McCormick*
Affiliation:
University of Georgia
*
Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.

Abstract

Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where {τ k} are the points of a renewal process and {Ak} are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1997 

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