On Piterbarg Max-Discretisation Theorem for Standardised Maximum of Stationary Gaussian Processes

Détails

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Etat: Public
Version: de l'auteur⸱e
ID Serval
serval:BIB_EA3345D9E0C9
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
On Piterbarg Max-Discretisation Theorem for Standardised Maximum of Stationary Gaussian Processes
Périodique
Methodology and Computing in Applied Probability
Auteur⸱e⸱s
Tan Z., Hashorva E.
ISSN
1387-5841 (Print)
1573-7713 (Electronic)
Statut éditorial
Publié
Date de publication
2014
Peer-reviewed
Oui
Volume
16
Numéro
1
Pages
169-185
Langue
anglais
Résumé
With motivation from Husler (Extremes 7:179-190, 2004) and Piterbarg (Extremes 7:161-177, 2004) in this paper we derive the joint limiting distribution of standardised maximum of a continuous, stationary Gaussian process and the standardised maximum of this process sampled at discrete time points. We prove that these two random sequences are asymptotically complete dependent if the grid of the discrete time points is sufficiently dense, and asymptotically independent if the grid is sufficiently sparse. We show that our results are relevant for computational problems related to discrete time approximation of the continuous time maximum.
Mots-clé
Extreme values, Piterbarg max-discretisation theorem, Studentised maxima, Piterbarg inequality, Approximation of random processes
Web of science
Open Access
Oui
Création de la notice
13/09/2012 22:47
Dernière modification de la notice
20/08/2019 16:12
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