Extremes of homogeneous Gaussian random fields

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Etat: Public
Version: de l'auteur⸱e
ID Serval
serval:BIB_AB69033FCE83
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Extremes of homogeneous Gaussian random fields
Périodique
Journal of Applied Probability
Auteur⸱e⸱s
Debicki  K., Hashorva  E., Soja-Kukieła  N.
ISSN
0021-9002
Statut éditorial
Publié
Date de publication
03/2015
Peer-reviewed
Oui
Volume
52
Numéro
1
Pages
55-67
Langue
anglais
Résumé
Let {X (s, t): s, t >= 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r (s, t) = cov(X(s, t), X(0, 0)) such that r(s, t) = 1 - vertical bar s vertical bar(alpha 1) - vertical bar t vertical bar(alpha 2) + o(vertical bar s vertical bar(alpha 1) + vertical bar t vertical bar(alpha 2)), s,t -> 0, with alpha 1, alpha 2 is an element of(0,2], and r (s, t) < 1 for (s, t) not equal (0, 0). In this contribution we derive an asymptotic expansion (as u -> infinity) of P(sup((sn1(u),tn2(u))is an element of[0,x]x[0,y]) X(s,t) <= u), where n(1)(u)n(2)(u) = u(2/alpha 1+2/alpha 2) Psi(u), which holds uniformly for (x, y) is an element of [A, B](2) with A, B two positive constants and Psi the survival function of an N(0, 1) random variable. We apply our findings to the analysis of extremes of homogeneous Gaussian fields over more complex parameter sets and a ball of random radius. Additionally, we determine the extremal index of the discretised random field determined by X (s, t).
Mots-clé
Gaussian random field, supremum, tail asymptoticy, external index, Berman condition, strong dependence
Web of science
Création de la notice
06/02/2014 13:53
Dernière modification de la notice
21/08/2019 6:10
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