Local Times and Excursion Theory for Brownian Motion
A Tale of Wiener and Itô Measures
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Beschreibung
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.
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.
Both local times and excursion theory are usually discussed in much longer texts. We examine these topics in relation to readers’ basic knowledge of stochastic processes Presents interesting applications of excursion theory Similarly with local times of Brownian motion Includes supplementary material: sn.pub/extras
Autor*in
Ju-Yi Yen
Themen in »Local Times and Excursion Theory for Brownian Motion«
arcsine law excursion theory functionals of Brownian motion local times
Stimmen zu »Local Times and Excursion Theory for Brownian Motion«
“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 and self-contained introduction … which are suitable for graduate students with a basic knowledge of stochastic processes in continuous time. … the proofs are mostly carried out with many details and helpful references are given in each chapter.” (David Prömel, zbMATH 1364.60003, 2017)
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