Asymptotic behaviour of mean uniform norms for sequences of Gaussian processes and fields
type: Item
instance of: scholarly article
title: Asymptotic behaviour of mean uniform norms for sequences of Gaussian processes and fields
zbMATH Open document ID: 1120.60039
author: Oleg Seleznjev
published in: Extremes
publication date: 2007-05-29T00:00:00Z
review text: Let \(X_{n}(t),\;t\in T_{n},\;n\geq1\), be a sequence of Gaussian zero mean random functions with continuous realizations. Denote by \(M_{n}(T_{n})=\max_{t\in T_{n}}| X_{n}(t)|\) the uniform norm of \(X_{n}(\cdot),\;n\geq1\). The author studies the asymptotic behavior of the mean uniform norms \(EM_{n}(T_{n})\) as \(n\to\infty\) provided that the normalized uniform norms \(M_{n}(T_{n})\) converge in distribution and for the \(m\)-cube \(T_{n}=[0,d_{n}]^{m},\;m\geq1, d_{n}\to\infty\) as \(n\to\infty\). It is proved that under some conditions \((EM_{n}^{p})^{1/p}\sim (2\log n)^{1/2}\) as \(n\to\infty\). The author considers some applications of the obtained results and demonstrates the rate of convergence for several Gaussian processes and fields.
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60F25
zbMATH DE Number: 5158674
zbMATH Keywords: extreme values
zbMATH Keywords: Gaussian process
zbMATH Keywords: Gaussian field
zbMATH Keywords: uniform norm
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: s10687-006-7965-x
OpenAlex ID: W1991081107
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DOI: 10.1007/S10687-006-7965-X
description: scientific article; zbMATH DE number 5158674