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Point processes, regular variation and weak convergence

Published online by Cambridge University Press:  01 July 2016

Sidney I. Resnick
Sidney I. Resnick*
Affiliation:
Colorado State University
*
∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA.
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Abstract

A method is reviewed for proving weak convergence in a function-space setting when regular variation is a sufficient condition. Point processes and weak convergence techniques involving continuity arguments play a central role. The method is dimensionless and holds computations to a minimum. Many applications of the methods to processes derived from sums and maxima are given.

Keywords

EXTREME VALUESPARTIAL SUM PROCESSESSTABLE PROCESSESPOISSON PROCESSEXTREMAL PROCESSESΠ-VARIATIONSUBORDINATIONINVARIANCE PRINCIPLESCONTINUITY OF FUNCTIONALS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 1 , March 1986 , pp. 66 - 138
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Partially supported by NSF Grant MCS 78-00915 and MCS-820235. Portions of the initial version were completed while supported by a Lady Davis Fellowship at the Technion. Grateful acknowledgement is made to the Faculty of Industrial and Management Engineering, Technion, Haifa, Israel, for their hospitality.

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