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Extreme values of independent stochastic processes

Published online by Cambridge University Press:  14 July 2016

Bruce M. Brown
Affiliation:
La Trobe University
Sidney I. Resnick
Affiliation:
Stanford University

Abstract

The maxima of independent Weiner processes spatially normalized with time scales compressed is considered and it is shown that a weak limit process exists. This limit process is stationary, and its one-dimensional distributions are of standard extreme-value type. The method of proof involves showing convergence of related point processes to a limit Poisson point process. The method is extended to handle the maxima of independent Ornstein–Uhlenbeck processes.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1977 

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Footnotes

*

Support provided by NSF Grant OIP 75–14513 while on leave from Stanford University. The hospitality of CSIRO, Division of Mathematics and Statistics, Canberra and the Department of Statistics, SGS, Australian National University is gratefully acknowledged.

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