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Mathematics - Probability Theory and Stochastic Processes | Local Times and Excursion Theory for Brownian Motion - A Tale of Wiener and Itô Measures

Local Times and Excursion Theory for Brownian Motion

A Tale of Wiener and Itô Measures

Series: Lecture Notes in Mathematics, Vol. 2088

Yen, Ju-Yi, Yor, Marc

2013, IX, 135 p. 9 illus., 8 illus. in color.

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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

Related subjects » Probability Theory and Stochastic Processes

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