Local Times and Excursion Theory for Brownian Motion

A Tale of Wiener and Itô Measures

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book Local Times and Excursion Theory for Brownian Motion by Ju-Yi Yen, Marc Yor, Springer International Publishing
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Author: Ju-Yi Yen, Marc Yor ISBN: 9783319012704
Publisher: Springer International Publishing Publication: October 1, 2013
Imprint: Springer Language: English
Author: Ju-Yi Yen, Marc Yor
ISBN: 9783319012704
Publisher: Springer International Publishing
Publication: October 1, 2013
Imprint: Springer
Language: English

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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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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