Some aspects of Brownian motion
By: Marc Yor.
Series: Lectures in mathematics ETH Zürich
Publisher: Birkhäuser
Published: 1992
Place of publication: Basel; Boston
Language: eng
Subjects: Brownian motion processes
Description: These notes represent approximately the second half of lectures given by the author at ETH in a Nachdiplom course (winter term 1991-92), followed by six lectures in November and December 1993. They are organized in nine chapters, six of which are devoted to - expansion of filtration formulae, - Burkholder-Gundy inequalities up to any random time, - martingales which vanish on the zero set of Brownian motion, - the Azéma-Emery martingales and chaos representation, - the filtration of truncated Brownian motion, - attempts to characterize the Brownian filtration. The three remaining chapters concern principal value of diffusion local times, probabilistic representations of the Riemann zeta function, and progress made on some topics discussed in Part I. Most of the contents of this book are the objects of active research, centered on real-valued martingales and Brownian motion. This volume may be of interest to researchers either in probability theory or in more applied fields, such as mathematical finance.
Notes: Includes bibliographical references and index.
Table of contents: title: pt. 1. Some special functions; title: pt. 2. Some recent martingale problems.