Extremal theory for stochastic processes
type: Item
instance of: scholarly article
title: Extremal theory for stochastic processes
zbMATH Open document ID: 0648.60039
author: Holger Rootzén
author: M. Ross Leadbetter
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: The authors present a review of the principal results in and related to the distributional theory of extremes of stationary sequences and processes. The review is given in three areas: extremes of sequences of independent, identically distributed random variables, extremes of stationary sequences and extremes of stationary continuous-parameter processes. Significant ideas and methods are described rather than details. In particular, the centrality of convergence results for point processes associated with extremes (such as exceedances and upcrossings) is emphasized. In many cases the details may be found in the book by the authors and \textit{G. Lindgren}, Extremes and related properties of random sequences and processes. (1983; Zbl 0518.60021). Applications are given to particular classes of processes (e.g., normal sequences and processes, regenerative and Markov sequences, moving averages, diffusion processes), and connections with the central limit problem of convergence of sums to nonnormal stable distributions are indicated.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60-02
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4058536
zbMATH Keywords: theory of extremes of stationary sequences and processes
zbMATH Keywords: convergence results for point processes
zbMATH Keywords: moving averages
zbMATH Keywords: central limit problem
zbMATH Keywords: nonnormal stable distributions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991767
OpenAlex ID: W2076877070
DOI: 10.1214/AOP/1176991767
description: scientific article; zbMATH DE number 4058536