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A note on the point processes of rare events

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

J. Hüsler  and
M. Schmidt
J. Hüsler*
Affiliation:
University of Bern
M. Schmidt*
Affiliation:
University of Bern
*
∗Postal address for both authors: Universität Bern, Institut für Mathematische Statistik und Versicherungslehre, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
∗Postal address for both authors: Universität Bern, Institut für Mathematische Statistik und Versicherungslehre, Sidlerstrasse 5, CH-3012 Bern, Switzerland.
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Abstract

We discuss the limits of point processes which are generated by a triangular array of rare events. Such point processes are motivated by the exceedances of a high boundary by a random sequence since exceedances are rare events in this case. This application relates the problem to extreme value theory from where the method is used to treat the asymptotic approximation of these point processes. The presented general approach extends, unifies and clarifies some of the various conditions used in the extreme value theory.

Keywords

RARE EVENTSEXTREMESEXCEEDANCESPOISSON PROCESSMIXING CONDITIONS

MSC classification

Primary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 654 - 663
Copyright
Copyright © Applied Probability Trust 1996 

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