Continuous martingales and Brownian motion (Grundlehren der mathematischen Wissenschaften) - Hardcover

Revuz, D

Hardcover

ISBN 10: 3540521674 ISBN 13: 9783540521679

Publisher: Springer-Verlag, 1991

Synopsis

This work provides a detailed study of Brownian motion, via the Ito stochastic calculus of continuous processes such as diffusions and continuous semi-martingales. It aims to facilitate the reading and understanding of research papers in this area, and will be of interest both to graduate students and to more advanced readers, either working primarily with stochastic processes, or doing research in an area involving stochastic processes, such as mathematical physics or economics. The emphasis is on methods, rather than generality. After the first introduction, each chapter introduces a new method or idea - stochastic integration, local times, excursions, weak convergence - and describes its applications to Brownian motion. A feature of the text is the large number of exercises which provide additional results. These have been designed to help the reader master the subject more easily.

About this title

Review:

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)

About this edition

• Publisher: Springer-Verlag
• Publication date: 1991
• ISBN 10: 3540521674
• ISBN 13: 9783540521679
• Binding: Hardcover
• Number of pages: 533