Stochastic integration with jumps

Author(s)

Bibliographic Information

Stochastic integration with jumps

Klaus Bichteler

（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 89）

Cambridge University Press, 2002

  • : hardback

Available at  / 72 libraries

Search this Book/Journal

Note

Bibliography: p. 477-482

Includes indexes

Description and Table of Contents

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 caglad 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.

Table of Contents

  • 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.

by "Nielsen BookData"

Related Books： 1-1 of 1

Details

Page Top