Stochastic Integration with Jumps

ISBN-13: 9780521811293 / Angielski / Twarda / 2002 / 516 str.

Klaus Bichteler; G. -C Rota; B. Doran

Opis

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 caglad integrands pathwise.

Recenzje

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

Spis treści

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.