Continuous Martingales and Brownian Motion

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.

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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 have been made in relation to the material found in this book. This shows how very alive the studies of, and around, Brownian motion are.