Stochastic Integration Theory [Hardcover]

This graduate level text covers the theory of stochastic integration, an important area of mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in mathematics, statistics, probability, mathematical finance, and economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and important examples (Brownian motion, Poisson process).

1. Stochastic processes
2. Stochastic integration with locally square-integrable martingales
3. The structure of local martingales
4. General theory of stochastic integration
5. Some other theorems
6. Ito's formula
7. Processes with independent increments
Appendices
A. Results from measure theory
B. Wiener processes
C. Poisson processes

This monograph gives a comprehensive exposition of stochastic calculus and can be used as a textbook for graduate students with a good knowledge of measure-theoretic probability and mathematical analysis...Although the material presented in this book can be found in other monographs on the subject, it can of interest for a wide readership, mainly due to the plenty of clarifying examples and the very detailed proofs of the results. --Mathematical Reviews