Large deviations of Shepp statistics for fractional Brownian motion

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Etat: Public
Version: de l'auteur
ID Serval
serval:BIB_B529358D3324
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Large deviations of Shepp statistics for fractional Brownian motion
Périodique
Statistics & Probability Letters
Auteur(s)
Hashorva E., Tan Z.
ISSN
0167-7152 (Print)
Statut éditorial
Publié
Date de publication
2013
Peer-reviewed
Oui
Volume
83
Numéro
10
Pages
2242-2247
Langue
anglais
Résumé
Define the incremental fractional Brownian field Z(H)(tau, S) = B-H (S+tau) By (S), H E (0, 1), where B-H(s) is a standard fractional Brownian motion with Hurst index H is an element of (0, 1). In this paper we derive the exact asymptotic behaviour of the maximum M-H (T) = max((tau,s)is an element of[0,1]x[0,T]) Z(H(tau, S)) for any H is an element of (0,1/2) complimenting thus the result of Zholud (2008) which establishes the exact tail asymptotic behaviour of M-1/2 (T).
Mots-clé
Shepp statistics, Scan statistics, Exact asymptotics, Extremes, Fractional Brownian motion
Web of science
Création de la notice
12/06/2013 11:07
Dernière modification de la notice
20/08/2019 15:23
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