Stochastic Integration ith Jumps [Hardcover]

The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.Stochastic processes with jumps and random measures can be expected to gain importance as drivers in applications like financial mathematics and signal processing. This comprehensive treatise pro vides their complete integration theory. 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.Stochastic processes with jumps and random measures can be expected to gain importance as drivers in applications like financial mathematics and signal processing. This comprehensive treatise pro vides their complete integration theory. 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.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 il³*