Buch, Englisch, Band 89, 516 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 775 g
Buch, Englisch, Band 89, 516 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 775 g
Reihe: Encyclopedia of Mathematics and its Applications
ISBN: 978-0-521-14214-4
Verlag: Cambridge University Press
• 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
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 c…gl…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.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
- Mathematik | Informatik Mathematik Stochastik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
Weitere Infos & Material
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.
