Stochastic Integration with Jumps
Edition: 1st edition
Publisher: Cambridge University Press
Published: May 13, 2002
Language: eng
Format: Hardcover
Number of pages: 512
ISBN-13: 9780521811293
Subjects: Calculus & mathematical analysis; Stochastic integrals; Differential Equations; Stochastic Processes; Mathematics; Science/Mathematics; Probability & Statistics - General; Mathematics / Differential Equations; Jump processes
First sentence: Stochastic Integration and Stochastic Differential Equations (SDEs) appear in analysis in various guises.
Description: 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.
Notes: Encyclopedia of Mathematics and its Applications