Stochastic Integration with Jumps
Stochastic Integration with Jumps
Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of cà glà d integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical engineering and finance who need to use stochastic differential equations.
- Contains the most general stochastic integration theory, applicable to both semimartingales and random measures
- Comprehensive: contains complete proofs for everything that goes beyond a first graduate course in anlysis
- Over 700 exercises
Reviews & endorsements
Review of the hardback: 'The material in the book is presented well: it is detailed, motivation is stressed throughout and the text is written with an enjoyable pinch of dry humour.' Evelyn Buckwar, Zentralblatt MATH
Review of the hardback: 'The highlights of the monograph are: Girsanov-Meyer theory on shifted martingales, which covers both the Wiener and Poisson setting; a Doob-Meyer decomposition statement providing really deep information that the objects that can go through the Daniell-like construction of the stochastic. This is an excellent and informative monograph for a general mathematical audience.' EMS
Product details
March 2011Adobe eBook Reader
9780511889288
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- 1. Introduction
- 2. Integrators and martingales
- 3. Extension of the integral
- 4. Control of integral and integrator
- 5. Stochastic differential equations
- Appendix A. Complements to topology and measure theory
- Appendix B. Answers to selected problems
- References
- Index.
