On Piterbarg's max-discretisation theorem for multivariate stationary Gaussian processes

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Etat: Public
Version: de l'auteur⸱e
ID Serval
serval:BIB_0E398DD87431
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
On Piterbarg's max-discretisation theorem for multivariate stationary Gaussian processes
Périodique
Journal of Mathematical Analysis and Applications
Auteur⸱e⸱s
Tan Z., Hashorva E.
ISSN
0022-247X (Print)
Statut éditorial
Publié
Date de publication
2014
Peer-reviewed
Oui
Volume
409
Numéro
1
Pages
299-314
Langue
anglais
Résumé
Let {X (t), t >= 0} be a stationary Gaussian process with zero-mean and unit variance. A deep result derived in Piterbarg (2004) [23], which we refer to as Piterbarg's max-discretisation theorem gives the joint asymptotic behaviour (T -> infinity) of the continuous time maximum M(T) = max(t is an element of[0,T]) X(t), and the maximum M-delta(T) = max(t is an element of R(delta)) X(t), with R(delta) subset of [0, T] a uniform grid of points of distance delta = delta(T). Under some asymptotic restrictions on the correlation function Piterbarg's max-discretisation theorem shows that for the limit result it is important to know the speed delta(T) approaches 0 as T -> infinity. The present contribution derives the aforementioned theorem for multivariate stationary Gaussian processes.
Mots-clé
Gaussian process, Piterbarg discretisation, Limit theorem
Web of science
Création de la notice
11/07/2013 7:43
Dernière modification de la notice
20/08/2019 13:35
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