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Local times and excursion theory for Brownian motion : a tale of wiener and itô measures

Auteur : Ju-Yi Yen; Marc Yor
Éditeur: Cham, Switzerland : Springer, ©2013.
Collection: Lecture notes in mathematics (Springer-Verlag), 2088.
Édition/format:   Livre électronique : Document : AnglaisVoir toutes les éditions et tous les formats
Base de données:WorldCat
Résumé:
This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the  Lire la suite...
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Détails

Genre/forme: Electronic books
Format – détails additionnels: Printed edition:
Type d’ouvrage: Document, Ressource Internet
Type de document: Ressource Internet, Fichier d'ordinateur
Tous les auteurs / collaborateurs: Ju-Yi Yen; Marc Yor
ISBN: 9783319012704 3319012703
Numéro OCLC: 859575095
Description: 1 online resource (ix, 135 pages) : illustrations.
Contenu: Prerequisites --
Part I: Local Times of Continuous Semimartingales. The Existence and Regularity of Semimartingale Local Times --
Lévy's Representation of Reflecting BM and Pitman's Representation of BES(3) --
Paul Lévy's Arcsine Laws --
Part II: Excursion Theory for Brownian Paths. Brownian Excursion Theory: A First Approach --
Two Descriptions of n: Itô's and Williams' --
A Simple Path Decomposition of Brownian Motion Around Time t = 1 --
The Laws of, and Conditioning with Respect to, Last Passage Times --
Integral Representations Relating W and n --
Part III: Some Applications of Excursion Theory. The Feynman-Kac Formula and Excursion Theory --
Some Identities in Law.
Titre de collection: Lecture notes in mathematics (Springer-Verlag), 2088.
Responsabilité: Ju Yi Yen, Marc Yor.

Résumé:

This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.

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Synopsis de l’éditeur

"The lecture notes provide an elementary and brief introduction to local times for continuous semimartingales and excursion theory for Brownian motion. ... The lecture notes are an easily accessible Lire la suite...

 
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