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The extremal index for a Markov chain

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Richard L. Smith
Richard L. Smith*
Affiliation:
University of Surrey
*
∗ Present address: Department of Statistics, University of North Carolina, Chapel Hill, NC 27599–3260, USA.
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Abstract

The paper presents a method of computing the extremal index for a discrete-time stationary Markov chain in continuous state space. The method is based on the assumption that bivariate margins of the process are in the domain of attraction of a bivariate extreme value distribution. Scaling properties of bivariate extremes then lead to a random walk representation for the tail behaviour of the process, and hence to computation of the extremal index in terms of the fluctuation properties of that random walk. The result may then be used to determine the asymptotic distribution of extreme values from the Markov chain.

Keywords

HARRIS CHAINSMULTIVARIATE EXTREME VALUE DISTRIBUTIONSWIENER–HOPF INTEGRAL EQUATION

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 37 - 45
Copyright
Copyright © Applied Probability Trust 1992 

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