© 1991

Continuous Martingales and Brownian Motion


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

Table of contents

  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

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).


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

  1. 1.Département de MathématiquesUniversité de Paris VIIParis Cedex 05France
  2. 2.Laboratoire de ProbabilitésUniversité Pierre et Marie CurieParis Cedex 05France

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