Boundary noncrossings of additive Wiener fields

Détails

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Etat: Serval
Version: de l'auteur
ID Serval
serval:BIB_CD06405DABD4
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Boundary noncrossings of additive Wiener fields
Périodique
Lithuanian Mathematical Journal
Auteur(s)
Hashorva E., Mishura Y.
ISSN
0363-1672 (Print)
1573-8825 (Online)
Statut éditorial
Publié
Date de publication
2014
Peer-reviewed
Oui
Volume
54
Numéro
3
Pages
277-289
Langue
anglais
Résumé
Let {W (i) (t), t a a"e(+)}, i = 1, 2, be two Wiener processes, and let W (3) = {W (3)(t), t a a"e (+) (2) } be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower bounds for the boundary noncrossing probability P (f) = P{W (1)(t (1)) + W (2)(t (2)) + W (3)(t) + f(t) a parts per thousand currency sign u(t), t a a"e (+) (2) }, where f, u : a"e (+) (2) -> a"e are two general measurable functions. We further show that, for large trend functions gamma f > 0, asymptotically, as gamma -> a, P (gamma f) is equivalent to , where is the projection of f onto some closed convex set of the reproducing kernel Hilbert space of the field W(t) = W (1)(t (1)) + W (2)(t (2)) + W (3)(t). It turns out that our approach is also applicable for the additive Brownian pillow.
Mots-clé
Boundary noncrossing probability, Reproducing kernel Hilbert space, Additive Wiener field, Polar cones, Logarithmic asymptotics, Brownian sheet, Brownian pillow
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Création de la notice
10/07/2014 0:07
Dernière modification de la notice
03/03/2018 21:29
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