Overview

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.

Full Product Details

Author:   Roger Mansuy ,  Marc Yor
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2008 ed.
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783540223474

ISBN 10:   3540223479
Pages:   200
Publication Date:   16 September 2008
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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 Lévy’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.

Reviews

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)

Author Information

"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""."

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions