Aspects of Brownian Motion

Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results regarding Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including 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. In addition to students and lecturers, the book addresses the interests of a wide spectrum of researchers, from core probability theory all the way to applied fields such as polymer physics and mathematical finance.