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Maxima and exceedances of stationary Markov chains

Published online by Cambridge University Press:  01 July 2016

Holger Rootzén
Holger Rootzén*
Affiliation:
University of Copenhagen
*
∗Present address: Department of Mathematical Statistics, University of Lund and Lund Institute of Technology, Box 118, S-221 00 Lund, Sweden.
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Abstract

Recent work by Athreya and Ney and by Nummelin on the limit theory for Markov chains shows that the close connection with regeneration theory holds also for chains on a general state space. Here this is used to study extremal behaviour of stationary (or asymptotically stationary) Markov chains. Many of the results center on the ‘clustering’ of extremes of adjacent values of the chains. In addition one criterion for convergence of extremes of general stationary sequences is derived. The results are applied to waiting times in the GI/G/1 queue and to autoregressive processes.

Keywords

REGENERATIVE PROCESSESCLUSTERING OF EXTREME VALUESPOINT PROCESS OF EXCEEDANCESSTATIONARY SEQUENCESGI/G/1 QUEUEAUTOREGRESSIVE PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 20 , Issue 2 , June 1988 , pp. 371 - 390
Copyright
Copyright © Applied Probability Trust 1988 

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