Continuous Martingales and Brownian Motion (Grundlehren der mathematischen Wissenschaften (293))

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. 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 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions. "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....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." BULLETIN OF THE L.M.S. Describes a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. This book explains the theory, presenting further developments as exercises. It is suitable for graduate students starting out on research in probability. This detailed study of Brownian motion via Ito stochastic calculus has been revised and updated to include new research material. A large number of exercises are featured which give additional results, and new methods or ideas are discussed in each chapter. In this chapter, we review a few basic facts, mainly from integration and classical probability theories, which will be used throughout the book without further ado. Daniel Revuz, Marc Yor. Includes Bibliographical References (p. [523]-548) And Indexes. Daniel Revuz, Marc Yor. Includes Bibliographical References (p. [553]-590) And Index.