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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.
List of contents
Prerequisites.- Local times of continuous semimartingales.- Excursion theory for Brownian paths.- Some applications of Excursion Theory.- Index.
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 same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.
Additional text
“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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"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)
