Extremes of a class of non-homogeneous Gaussian random fields

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Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Extremes of a class of non-homogeneous Gaussian random fields
Journal
Annals of Probability
Author(s)
Debicki  K., Hashorva  E., Ji  L.
ISSN
0091-1798
Publication state
Published
Issued date
03/2016
Peer-reviewed
Oui
Volume
44
Number
2
Pages
984-1012
Language
english
Abstract
This contribution establishes exact tail asymptotics of sup((s,t)) is an element of E X(s,t) for a large class of nonhomogeneous Gaussian random fields X on a bounded convex set E subset of R-2, with variance function that attains its maximum on a segment on E. These findings extend the classical results for homogeneous Gaussian random fields and Gaussian random fields with unique maximum point of the variance. Applications of our result include the derivation of the exact tail asymptotics of the Shepp statistics for stationary Gaussian processes, Brownian bridge and fractional Brownian motion as well as the exact tail asymptotic expansion for the maximum loss and span of stationary Gaussian processes.
Keywords
Extremes, nonhomogeneous Gaussian random fields, Shepp statistics, fractional Brownian motion, maximum loss, span of Gaussian processes, Pickands constant, Piterbarg constant, generalized Pickands-Piterbarg constant
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08/12/2014 23:09
Last modification date
20/08/2019 13:06
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