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The distributions of cluster functionals of extreme events in a dth-order Markov chain

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Seokhoon Yun
Seokhoon Yun*
Affiliation:
University of Suwon
*
∗Postal address: Department of Applied Statistics, University of Suwon, Suwon, Kyonggi-do 445–743, South Korea. Email address: syun@stat.suwon.ac.kr
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Abstract

The paper concerns the asymptotic distributions of cluster functionals of extreme events in a dth-order stationary Markov chain {Xn, n = 1,2,…} for which the joint distribution of (X1,…,Xd+1) is absolutely continuous. Under some distributional assumptions for {Xn}, we establish weak convergence for a class of cluster functionals and obtain representations for the asymptotic distributions which are well suited for simulation. A number of examples important in applications are presented to demonstrate the usefulness of the results.

Keywords

Extreme eventscluster functionalsdth-order stationary Markov chain

MSC classification

Primary: 60G70: Extreme value theory; extremal processes 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 29 - 44
Copyright
Copyright © 2000 by The Applied Probability Trust 

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