Dȩbicki, K, Hashorva, E and Ji, L orcid.org/0000-0002-7790-7765 (2016) Extremes of a class of nonhomogeneous Gaussian random fields. The Annals of Probability, 44 (2). pp. 984-1012. ISSN 0091-1798
Abstract
This contribution establishes exact tail asymptotics of sup(s,t)∈E X(s,t) for a large class of nonhomogeneous Gaussian random fields X on a bounded convex set E⊂R2, 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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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 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Jul 2019 13:57 |
Last Modified: | 03 Jul 2019 13:57 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/14-AOP994 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147165 |