Continuous martingales and Brownian motion
Revuz, Daniel
Continuous martingales and Brownian motion - Berlin Springer 1999 - xi, 606 p. ill. Includes bibliographical references and index - A series of comprehensive studies in mathematics 293 .
Table of contents
Ch. 0. Preliminaries --
Ch. I. Introduction --
Ch. II. Martingales --
Ch. III. Markov Processes --
Ch. IV. Stochastic Integration --
Ch. V. Representation of Martingales --
Ch. VI. Local Times --
Ch. VII. Generators and Time Reversal --
Ch. VIII. Girsanov's Theorem and First Applications --
Ch. IX. Stochastic Differential Equations --
Ch. X. Additive Functionals of Brownian Motion --
Ch. XI. Bessel Processes and Ray-Knight Theorems --
Ch. XII. Excursions --
Ch. XIII. Limit Theorems in Distribution.
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.
https://link.springer.com/book/10.1007/978-3-662-06400-9
9783642084003
Brownian motion processes
Martingales - Mathematics
Stochastic Integration
519.287 / R3C6
Continuous martingales and Brownian motion - Berlin Springer 1999 - xi, 606 p. ill. Includes bibliographical references and index - A series of comprehensive studies in mathematics 293 .
Table of contents
Ch. 0. Preliminaries --
Ch. I. Introduction --
Ch. II. Martingales --
Ch. III. Markov Processes --
Ch. IV. Stochastic Integration --
Ch. V. Representation of Martingales --
Ch. VI. Local Times --
Ch. VII. Generators and Time Reversal --
Ch. VIII. Girsanov's Theorem and First Applications --
Ch. IX. Stochastic Differential Equations --
Ch. X. Additive Functionals of Brownian Motion --
Ch. XI. Bessel Processes and Ray-Knight Theorems --
Ch. XII. Excursions --
Ch. XIII. Limit Theorems in Distribution.
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.
https://link.springer.com/book/10.1007/978-3-662-06400-9
9783642084003
Brownian motion processes
Martingales - Mathematics
Stochastic Integration
519.287 / R3C6