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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
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.
Content Level »Research
Keywords »arcsine law - excursion theory - functionals of Brownian motion - local times