Stochastic Integration with Jumps

Encyclopedia of Mathematics and its Applications

Klaus Bichteler

502 pages, parution le 16/05/2002

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Résumé

Stochastic processes with jumps and random measures are gaining importance as drivers in applications like financial mathematics and signal processing. This book 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 to 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.

Contents

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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Klaus Bichteler
Parution	16/05/2002
Nb. de pages	502
Format	16 x 24
Couverture	Relié
Poids	893g
Intérieur	Noir et Blanc
EAN13	9780521811293
ISBN13	978-0-521-81129-3