Exact asymptotics for Boundary crossings of the brownian bridge with trend with application to the Kolmogorov test

Détails

ID Serval
serval:BIB_2048F54529BC
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Exact asymptotics for Boundary crossings of the brownian bridge with trend with application to the Kolmogorov test
Périodique
Annals of the Institute of Statistical Mathematics
Auteur(s)
Bischoff W., Hashorva E., Hüsler J., Miller F.
ISSN
0020-3157
1572-9052 ([electronic])
Statut éditorial
Publié
Date de publication
2003
Peer-reviewed
Oui
Volume
55
Numéro
4
Pages
849-864
Langue
anglais
Résumé
We consider a boundary crossing probability of a Brownian bridge B-0 and a piecewise linear boundary function u(t) - gammah(t). The main result of this paper is an asymptotic expansion for gamma --> infinity of the boundary crossing probability that B-0(t) is larger than the piecewise linear boundary function u(t) - gammah(t) for some t. Such probabilities occur for instance in the context of change point problems when the Kolmogorov test is used. Examples are discussed showing that the approximation is rather accurate even for small positive gamma values.
Mots-clé
Brownian bridge with trend, Boundary crossing probability, Exact asymptotics, Extreme values, Large deviations, Kolmogorov test
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Création de la notice
03/09/2010 11:49
Dernière modification de la notice
20/08/2019 13:56
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