# Continuous Martingales and Brownian Motion

• Daniel Revuz
• Marc Yor
Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 293)

1. Front Matter
Pages I-IX
2. Daniel Revuz, Marc Yor
Pages 1-13
3. Daniel Revuz, Marc Yor
Pages 14-47
4. Daniel Revuz, Marc Yor
Pages 48-73
5. Daniel Revuz, Marc Yor
Pages 74-112
6. Daniel Revuz, Marc Yor
Pages 113-167
7. Daniel Revuz, Marc Yor
Pages 168-205
8. Daniel Revuz, Marc Yor
Pages 206-258
9. Daniel Revuz, Marc Yor
Pages 259-300
10. Daniel Revuz, Marc Yor
Pages 301-337
11. Daniel Revuz, Marc Yor
Pages 338-370
12. Daniel Revuz, Marc Yor
Pages 371-408
13. Daniel Revuz, Marc Yor
Pages 409-434
14. Daniel Revuz, Marc Yor
Pages 435-471
15. Daniel Revuz, Marc Yor
Pages 472-498
16. Back Matter
Pages 499-536

### Introduction

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).

### Keywords

Brownian motion Functionals Generator Martingal Martingale brownsche Bewegung diffusion ergodic theory local time probability probability theory stochastic calculus stochastic differential equation stochastic processes stochastische Integration

#### Authors and affiliations

• Daniel Revuz
• 1
• Marc Yor
• 2
1. 1.Département de MathématiquesUniversité de Paris VIIParis Cedex 05France
2. 2.Laboratoire de ProbabilitésUniversité Pierre et Marie CurieParis Cedex 05France

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-662-21726-9
• Copyright Information Springer-Verlag Berlin Heidelberg 1991
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-662-21728-3
• Online ISBN 978-3-662-21726-9
• Series Print ISSN 0072-7830