Stochastic integration with jumps
著者
書誌事項
Stochastic integration with jumps
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 89）
Cambridge University Press, 2010
- : pbk
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注記
"First published 2002. This digitally printed version 2010"--T.p. verso
Bibliography: p. 477-482
Includes indexes
内容説明・目次
内容説明
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 caglad 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.
目次
- 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.
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