Extremal behaviour of stationary Markov chains with applications
type: Item
instance of: scholarly article
title: Extremal behaviour of stationary Markov chains with applications
zbMATH Open document ID: 0806.60041
author: Roland Perfekt
published in: The Annals of Applied Probability
publication date: 1995-02-14T00:00:00Z
review text: The paper concerns the extremal behaviour of real-valued, stationary Markov chains. The author finds conditions for convergence in distribution of the multilevel exceedance point processes for general stationary sequences. These conditions are convenient for applications to Markov chains. The results obtained extend the one-level result of \textit{H. Rootzén} [Adv. Appl. Probab. 20, No. 2, 371-390 (1988; Zbl 0654.60023)] to the multilevel case and to complete convergence. Next, the author uses the results together with ideas from a paper by \textit{R. L. Smith} [J. Appl. Probab. 29, No. 1, 37-45 (1992; Zbl 0759.60059)] to investigate extremal properties of a large class of stationary Markov chains. Finally, he presents two examples which deal with an AR(1) process with uniform margins and with solutions of a first order stochastic difference equation with random coefficients.
reviewed by: Wiesław Dziubdziela
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 639117
zbMATH Keywords: extremal behaviour
zbMATH Keywords: conditions for convergence in distribution
zbMATH Keywords: multilevel exceedance point processes
zbMATH Keywords: complete convergence
zbMATH Keywords: stochastic difference equation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005071
OpenAlex ID: W1982275270
DOI: 10.1214/AOAP/1177005071
description: scientific article; zbMATH DE number 639117