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

Author: Ju-Yi Yen; Marc Yor
Publisher: Cham, Switzerland : Springer, ©2013.
Series: Lecture notes in mathematics (Springer-Verlag), 2088.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ju-Yi Yen; Marc Yor
ISBN: 9783319012704 3319012703
OCLC Number: 859575095
Description: 1 online resource (ix, 135 pages) : illustrations.
Contents: 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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2088.
Responsibility: Ju Yi Yen, Marc Yor.
More information:

Abstract:

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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