Diffusions, Markov processes, and martingales
- L.C.G. Rogers and David Williams.
- 2nd ed.
- Cambridge, U.K. ; New York : Cambridge University Press, 2000.
- Physical description
- 2 v. : ill. ; 23 cm.
- Cambridge mathematical library.
Math & Statistics Library
Library has: v.2
|QA274.7 .W54 2000 V.2||Unknown|
- Includes bibliographical references and indexes.
- Some frequently used notation-- 1. Brownian motion-- Part I. Introduction-- 2. Basics about Brownian motion-- 3. Brownian motion in higher dimensions-- 4. Gaussian processes and Levy processes-- Part II. Some Classical Theory-- 5. Basic measure theory-- 6. Basic probability theory-- 7. Stochastic processes-- 8. Discrete-parameter martingale theory-- 9. Continuous-parameter martingale theory-- 10. Probability measure on Lusin spaces-- Part III. Markov Processes: 11. Transition functions and resolvents-- 12. Feller-Dynkin processes-- 13. Additive functionals-- 14. Approach to ray processes: the Martin boundary-- 15. Ray processes-- 16. Applications-- References-- Index.
- (source: Nielsen Book Data)9780521775946 20160611
- Some frequently used notation-- 4. Introduction to Ito calculus-- 4.1. Some motivating remarks-- 4.2. Some fundamental ideas: previsible processes, localization, etc.-- 4.3. The elementary theory of finite-variation processes-- 4.4. Stochastic integrals: the L2 theory-- 4.5. Stochastic integrals with respect to continuous semimartingales-- 4.6. Applications of Ito's formula-- 5. Stochastic differential equations and diffusions-- 5.1. Introduction-- 5.2. Pathwise uniqueness, strong SDEs, flows-- 5.3. Weak solutions, uniqueness in law-- 5.4. Martingale problems, Markov property-- 5.5. Overture to stochastic differential geometry-- 5.6. One-dimensional SDEs-- 5.7. One-dimensional diffusions-- 6. The general theory-- 6.1. Orientation-- 6.2. Debut and section theorems-- 6.3. Optional projections and filtering-- 6.4. Characterising previsible times-- 6.5. Dual previsible projections-- 6.6. The Meyer decomposition theorem-- 6.7. Stochastic integration: the general case-- 6.8. Ito excursion theory-- References-- Index.
- (source: Nielsen Book Data)9780521775939 20160611
- Publisher's Summary
- Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
(source: Nielsen Book Data)9780521775946 20160611
- This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
(source: Nielsen Book Data)9780521775939 20160611
- Supplemental links
Table of contents
- Reprint/reissue date
- Original date
- Cambridge mathematical library
- Originally published: Chichester, West Sussex, England ; New York : Wiley, c1994.
- 0521775949 (v. 1 : pbk.)
- 9780521775946 (v. 1 : pbk.)
- 0521775930 (v. 2 : pbk.)
- 9780521775939 (v. 2 : pbk.)
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