Semicontinuous processes in multi-dimensional extreme value theory
type: Item
instance of: scholarly article
title: Semicontinuous processes in multi-dimensional extreme value theory
zbMATH Open document ID: 0628.60035
DOI: 10.1016/0304-4149(87)90188-8
author: Tommy Norberg
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: The author provides a new framework for weak convergence of extremes for stationary random fields. He extends some well-known results in the one- dimensional theory, which can be found in the monograph by \textit{M. R. Leadbetter}, \textit{G. Lindgren} and \textit{H. Rootzén}, Extreme and related problems of random sequences and processes (1983; Zbl 0518.60021), to random fields. The emphasis is on the continuous-parameter case, although new results are obtained also for discrete parameter random fields. Concrete asymptotic results are given for the Gaussian fields. The main tools are some recent results of \textit{W. Vervaat} [cf. Random upper semicontinuous functions and extremal processes, Report MS-R8801, Centre for Mathematics and Computer Science, Amsterdam (1988)] and the author [Ann. Probab. 12, 726-732 (1984; Zbl 0545.60021) and Probab. Theory Relat. Fields 73, 281-297 (1986; Zbl 0581.60042)], concerning semicontinuous processes and random sets.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 4022265
zbMATH Keywords: weak convergence of extremes for stationary random fields
zbMATH Keywords: asymptotic results
zbMATH Keywords: Gaussian fields
reviewed by: Wiesław Dziubdziela
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90188-8
OpenAlex ID: W2087160567
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description: scientific article; zbMATH DE number 4022265