Stochastic Integration with Jumps

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.

המשפט הראשון: Stochastic Integration and Stochastic Differential Equations (SDEs) appear in analysis in various guises.

שנה

2002

שפה

English

הוצאה

Cambridge University Press

מהדורות

5

עמודים

512

ISBN

9780521811293

מקור הנתונים: Wikidata