The distribution of the maximum of particular random fields
type: Item
instance of: scholarly article
title: The distribution of the maximum of particular random fields
zbMATH Open document ID: 0604.60037
DOI: 10.1016/0304-4149(86)90123-7
author: B. L. Montgomery
author: Julia Abrahams
published in: Stochastic Processes and their Applications
publication date: 1986-01-01T00:00:00Z
review text: The authors consider the zero mean Gaussian random field X(t,s) with correlation function \[ R(\tau,\sigma)=EX(t,s)X(t+\tau,s+\sigma)=2^{- 1}[(1-| \tau |)^++(1-| \sigma |)^+]. \] They call it Slepian sum field. The distribution of max\(\{\) X(t,s),\(0\leq s,t\leq 1\}\) is evaluated. A special example is the process \(W(t,s)=2^{-1/2}(W_ 1(t)+W_ 2(s))\) where \(W_ 1\) and \(W_ 2\) are independent Wiener processes.
reviewed by: Pál Révész
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 3976003
zbMATH Keywords: Wiener sheet
zbMATH Keywords: distribution of maximum
zbMATH Keywords: Gaussian random field
zbMATH Keywords: Slepian sum field
MaRDI profile type: Publication
full work available at URL: 0304-4149(86)90123-7
OpenAlex ID: W1979091210
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description: scientific article; zbMATH DE number 3976003