Generalized Pickands constants and stationary max-stable processes

Détails

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Etat: Public
Version: de l'auteur⸱e
ID Serval
serval:BIB_9760DCC13F00
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Generalized Pickands constants and stationary max-stable processes
Périodique
Extremes
Auteur⸱e⸱s
Debicki K., Engelke S., Hashorva E.
ISSN
1386-1999
1572-915X
Statut éditorial
Publié
Date de publication
09/2017
Peer-reviewed
Oui
Volume
20
Numéro
3
Pages
493-517
Langue
anglais
Résumé
Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often unknown. Recently, Dieker and Yakir (Bernoulli, 20(3), 1600–1619, 2014) derived a novel representation of Pickands constant as a simple expected value that does not involve a limit operation. In this paper we show that the notion of Pickands constants and their corresponding Dieker–Yakir representations can be extended to a large class of stochastic processes, including general Gaussian and Lévy processes. We furthermore develop a link to extreme value theory and show that Pickands-type constants coincide with certain constants arising in the study of max-stable processes with mixed moving maxima representations.
Mots-clé
Statistics and Probability, Engineering (miscellaneous), Economics, Econometrics and Finance (miscellaneous), Statistics and Probability, Engineering (miscellaneous), Economics, Econometrics and Finance (miscellaneous)
Création de la notice
11/03/2017 11:58
Dernière modification de la notice
20/08/2019 14:59
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