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Almost sure relative stability of the maximum of a stationary sequence

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Philippe Naveau
Philippe Naveau*
Affiliation:
University of Colorado at Boulder
*
∗ Postal address: University of Colorado at Boulder, Department of Applied Mathematics, Boulder, CO 80309-0526, USA. Email address: philippe.naveau@colorado.edu
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Abstract

The almost sure convergence of the maximum of a strictly stationary sequence is studied. We show that, if a particular mixing condition, related to the asymptotic independence of maxima defined by O'Brien, is satisfied, then the maximum behaves asymptotically like the quantile F←(1-1/n) whenever the marginal tail distribution decreases quickly enough. A necessary condition for the almost sure convergence of the maximum is derived. Applications are also discussed.

Keywords

Maximumalmost sure relative stabilityasymptotic independence of maximablocking technique

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G10: Stationary processes 60G17: Sample path properties
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 3 , September 2003 , pp. 721 - 736
Copyright
Copyright © Applied Probability Trust 2003 

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