Diffusions, Markov processes, and martingales
 Responsibility
 L.C.G. Rogers and David Williams.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Cambridge, U.K. ; New York : Cambridge University Press, 2000.
 Physical description
 2 v. : ill. ; 23 cm.
 Series
 Cambridge mathematical library.
Access
Available online
Math & Statistics Library
Stacks
Library has: v.2
Call number  Status 

QA274.7 .W54 2000 V.2  Unknown 
More options
Creators/Contributors
 Author/Creator
 Rogers, L. C. G.
 Contributor
 Williams, D. (David), 1938
Contents/Summary
 Bibliography
 Includes bibliographical references and indexes.
 Contents

 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. Discreteparameter martingale theory 9. Continuousparameter martingale theory 10. Probability measure on Lusin spaces Part III. Markov Processes: 11. Transition functions and resolvents 12. FellerDynkin 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 finitevariation 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. Onedimensional SDEs 5.7. Onedimensional 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 selfcontained 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

Publisher description
Table of contents
Subjects
Bibliographic information
 Reprint/reissue date
 2000
 Original date
 1994
 Series
 Cambridge mathematical library
 Note
 Originally published: Chichester, West Sussex, England ; New York : Wiley, c1994.
 ISBN
 0521775949 (v. 1 : pbk.)
 9780521775946 (v. 1 : pbk.)
 0521775930 (v. 2 : pbk.)
 9780521775939 (v. 2 : pbk.)