Diffusions, Markov Processes and Martingales
Diffusions, Markov Processes and Martingales
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.
- Classic book, first time in paperback
- Intuitive and rigorous, so suited for graduate students and non-experts
- Comprehensive and up-to-date
Reviews & endorsements
'I welcome the paperback edition version of this masterfully written text.' Paul Embrechts, JASA
'The monograph as a whole is warmly recommended to post-PhD students of probability and will be welcomed as a good and reliable reference.' EMS
'… will be read with pleasure and advantage by experts in the field and its applications, as well as by those probabilists and others who wish to learn the subject … an exciting and enjoyable introduction to the rich ideas of the Itô calculus … there is nothing dry about this book, for its authors have already breathed life into a vibrant subject.' Mathematics Today
Product details
No date availablePaperback
9780521775939
496 pages
226 × 152 × 23 mm
0.66kg
Table of Contents
- 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.
