Aspects of Brownian Motion 2008th Edition

From the reviews:

“The reader will marvel at the authors’ knowledge and expertise. … the book makes clear that although the mathematical study of Brownian motion is almost one hundred years old, the directions for continued study and new investigations remain unlimited.” (Michael B. Marcus, Bulletin of the American Mathematical Society, Vol. 48 (3), July, 2011)

Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as:

– Gaussian subspaces of the Gaussian space of Brownian motion;

– Brownian quadratic funtionals;

– Brownian local times,

– Exponential functionals of Brownian motion with drift;

– Winding number of one or several Brownian motions around one or several points or a straight line, or curves;

– Time spent by Brownian motion below a multiple of its one-sided supremum.

Besides its obvious audience of students and lecturers the book also addresses the interests of researchers from core probability theory out to applied fields such as polymer physics and mathematical finance.