Overview
- Authors:
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Daniel Revuz
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Département de Mathématiques, Université de Paris VII, Paris Cedex 05, France
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Marc Yor
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Laboratoire de Probabilités, Université Pierre et Marie Curie, Paris Cedex 05, France
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Table of contents (14 chapters)
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Back Matter
Pages 499-536
About this book
This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of processes. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).
Authors and Affiliations
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Département de Mathématiques, Université de Paris VII, Paris Cedex 05, France
Daniel Revuz
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Laboratoire de Probabilités, Université Pierre et Marie Curie, Paris Cedex 05, France
Marc Yor
