Local Times and Excursion Theory for Brownian Motion

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.

Prerequisites. - Local times of continuous semimartingales. - Excursion theory for Brownian paths. - Some applications of Excursion Theory. - Index.