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AuthorRevuz, Daniel. author
TitleContinuous Martingales and Brownian Motion [electronic resource] / by Daniel Revuz, Marc Yor
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999
Edition Corrected Third Printing of the Third Edition
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Descript XIII, 602 p. online resource


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


0. Preliminaries -- I. Introduction -- II. Martingales -- III. Markov Processes -- IV. Stochastic Integration -- V. Representation of Martingales -- VI. Local Times -- VII. Generators and Time Reversal -- VIII. Girsanovโ{128}{153}s Theorem and First Applications -- IX. Stochastic Differential Equations -- X. Additive Functionals of Brownian Motion -- XI. Bessel Processes and Ray-Knight Theorems -- XII. Excursions -- XIII. Limit Theorems in Distribution -- ยง1. Gronwallโ{128}{153}s Lemma -- ยง2. Distributions -- ยง3. Convex Functions -- ยง4. Hausdorff Measures and Dimension -- ยง5. Ergodic Theory -- ยง6. Probabilities on Function Spaces -- ยง7. Bessel Functions -- ยง8. Sturm-Liouville Equation -- Index of Notation -- Index of Terms -- Catalogue

Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes


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