Models for stationary max-stable random fields
type: Item
instance of: scholarly article
title: Models for stationary max-stable random fields
zbMATH Open document ID: 1035.60054
DOI: 10.1023/A:1020977924878
author: M. Schlather
published in: Extremes
publication date: 2004-03-16T00:00:00Z
review text: The max-stable process \(Z\) is the limit process of maxima of i.i.d. random fields (processes). The author considers different methods of generating stationary max-stable processes on \(R^d\). For example, the following theorem is proved: Let \(Y\) be a stationary process on \(R^d\) with \(\mu= E\max\{0,Y(0)\}\in(0,\infty)\) and let \(\Pi\) be a Poisson process on \((0,\infty)\) with the intensity measure \(d\Lambda(s)=\mu^{-1}s^{-2}ds\). Then \(Z(x)=\max_{s\in\Pi} sY_s(x), \) where \(Y_s\) are i.i.d. copies of \(Y\), is a stationary max-stable process with unit Fréchet margins. A simulation technique for such processes is described.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 2059057
zbMATH Keywords: bivariate extreme value distribution
zbMATH Keywords: dependence function
zbMATH Keywords: rainfall modelling
describes a project that uses: R
MaRDI profile type: Publication
full work available at URL: a:1020977924878
OpenAlex ID: W1578338182
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description: scientific article; zbMATH DE number 2059057