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April, 1988 Extremal Theory for Stochastic Processes
M. R. Leadbetter, Holger Rootzen
Ann. Probab. 16(2): 431-478 (April, 1988). DOI: 10.1214/aop/1176991767


The purpose of this paper is to provide an overview of the asymptotic distributional theory of extreme values for a wide class of dependent stochastic sequences and continuous parameter processes. The theory contains the standard classical extreme value results for maxima and extreme order statistics as special cases but is richer on account of the diverse behavior possible under dependence in both discrete and continuous time contexts. Emphasis is placed on stationary cases but some departures from stationarity are considered. Significant ideas and methods are described rather than details, and, in particular, the nature and role of important underlying point processes (such as exceedances and upcrossings) are emphasized. Applications are given to particular classes of processes (e.g., normal, moving average) and connections with related theory (such as convergence of sums) are indicated.


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M. R. Leadbetter. Holger Rootzen. "Extremal Theory for Stochastic Processes." Ann. Probab. 16 (2) 431 - 478, April, 1988.


Published: April, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0648.60039
MathSciNet: MR929071
Digital Object Identifier: 10.1214/aop/1176991767

Primary: 60G10
Secondary: 60F05 , 60G15 , 60G17 , 60G55

Keywords: 60-02 , Extreme values , Point processes , Stationary processes

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 2 • April, 1988
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