by Marc Yor (Author), Marc Yor (Author), Roger Mansuy (Author)
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.
Format: Paperback
Pages: 214
Edition: 2008
Publisher: Springer
Published: 16 Sep 2008
ISBN 10: 3540223479
ISBN 13: 9783540223474
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)MARC YOR has been Professor at the Laboratoire de Probabilites et Modeles Aleatoires at the Universite Pierre et Marie Curie, Paris, since 1981, and a member of the Academie 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 Lycee 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 .
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