Part I: Local Times of Continuous Semimartingales. The Existence and Regularity of Semimartingale Local Times
Lévy's Representation of Reflecting BM and Pitman's Representation of BES(3)
Paul Lévy's Arcsine Laws
Part II: Excursion Theory for Brownian Paths. Brownian Excursion Theory: A First Approach
Two Descriptions of n: Itô's and Williams'
A Simple Path Decomposition of Brownian Motion Around Time t = 1
The Laws of, and Conditioning with Respect to, Last Passage Times
Integral Representations Relating W and n
Part III: Some Applications of Excursion Theory. The Feynman-Kac Formula and Excursion Theory
Some Identities in Law.
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. (source: Nielsen Book Data)