Description
Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about 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; Time spent by Brownian motion below a multiple of its one-sided supremum. MARC YOR has been Professor at the Laboratoire de Probabilits et Modles Alatoires at the Universit Pierre et Marie Curie, Paris, since 1981, and a member of the Acadmie des Sciences de Paris since 2003. His research interests – which are well illustrated in the present book – bear upon properties of Brownian functionals, either for pure or applied purposes. Recently, Marc Yor has also been working on the interface between number theory and random matrices. ROGER MANSUY has been teaching mathematics at the Lyce Louis le Grand, Paris, since 2006. He has been working with Marc Yor – who was the supervisor of Roger Mansuy’s PhD thesis – in recent years. Prior to the present volume he and Marc Yor collaborated in publishing volume 1873 of the series Lecture Notes in Mathematics entitled “Random Times and Enlargements of Filtration in a Brownian setting”. The Gaussian space of BM.- The laws of some quadratic functionals of BM.- Squares of Bessel processes and Ray-Knight theorems for Brownian local times.- An explanation and some extensions of the Ciesielski-Taylor identities.- On the winding number of planar BM.- On some exponential functionals of Brownian motion and the problem of Asian options.- Some asymptotic laws for multidimensional BM.- Some extensions of Paul Lvy’s arc sine law for BM.- Further results about reflecting Brownian motion perturbed by its local time at 0.- On principal values of Brownian and Bessel local times.- Probabilistic representations of the Riemann zeta function and some generalisations related to Bessel processes.
