Introduction to Stochastic Integration

Introduction to Stochastic Integration

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A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability.Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Itô s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman-Kac fun...