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

Inhalt

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