Stochastic Integration with Jumps

The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.

Klaus Bichteler (Author)

9780521811293, Cambridge University Press

Hardback, published 13 May 2002

516 pages
24.2 x 16.4 x 3.4 cm, 0.897 kg

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

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 càglàd 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.

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.

Subject Areas: Probability & statistics [PBT], Calculus & mathematical analysis [PBK]