Continuous Martingales and Brownian Motion

Produktbeschreibung

From the reviews: "This is a magnificent book! Its purpose is to describe
in considerable detail a variety of techniques used by probabilists in
the investigation of problems concerning Brownian motion. The great strength
of Revuz and Yor is the enormous variety of calculations carried out both
in the main text and also (by implication) in the exercises. ... This is
THE book for a capable graduate student starting out on research in probability:
the effect of working through it is as if the authors are sitting beside
one, enthusiastically explaining the theory, presenting further developments
as exercises, and throwing out challenging remarks about areas awaiting
further research..."Bull.L.M.S. 24, 4 (1992) Since the first edition in
1990, an impressive variety of advances has been made in relation to the
material found in this book. 

Inhaltsverzeichnis

From the contents:
Continous Martingales and Brownian Motions: Preliminaries
- Introduction
- Martingales
- Markov Processes
- Stochastic Integration
- Representation of Martingales
- Local Times
- Generators and Time Reversal
- Girsanov's Theorem and First Applications
- Stochastic Differential Equations
- Additive Functionals of Brownian Motion
- Bessel Processes and Ray-Knight Theorems
- Excursions
- Limit Theorems in Distribution
- Appendix
- Bibliography
- Index of Notation
- Index of Terms
- Catalogue 

Kritik

This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..." Bull.L.M.S. 24, 4 (1992)

From the reviews of the third edition:



"The authors have revised the second edition of their fundamental and impressive monograph on Brownian motion and continuous martingales ... . The presentation of this book is unique in the sense that a concise and well-written text is complemented by a long series of detailed exercises. ... This third edition contains some additional exercises related to recent advances in the subject. ... is a valuable update of this basic reference book, which has been very helpful for researchers and students ... ." (David Nualart, Zentralblatt MATH, Vol. 1087, 2006)