Roger Mansuy, Marc Yor

Aspects of Brownian Motion (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 200
• Erscheinungstermin: 16. September 2008
• Englisch
• ISBN-13: 9783540499664
• Artikelnr.: 44130057

Autorenporträt

MARC YOR has been Professor at the Laboratoire de Probabilités et Modèles Aléatoires at the Université Pierre et Marie Curie, Paris, since 1981, and a member of the Académie 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 Lycée 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".

Inhaltsangabe

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.

Rezensionen

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)