Introduction to Stochastic Integration

"Introduction to Stochastic Integration" is a comprehensive textbook that provides a clear and accessible introduction to stochastic integration and stochastic differential equations. It is aimed at students and professionals who already have a basic understanding of probability theory. The book combines fundamental theoretical developments with practical applications, making it ideal for use in a graduate course in stochastic analysis. The modern approach to stochastic integration is supported by the definition of the stochastic integral for predictable integrands and local martingales. Topics covered include the characterization of Brownian motion, Hermite polynomials of martingales, as well as the Feynman-Kac functional and the Schrödinger equation. The second edition also includes new discussions on the Cameron-Martin-Girsanov transformation and offers an introduction to stochastic differential equations, supplemented by numerous exercises for the classroom. This book is a valuable resource for mathematicians, statisticians, economists, and engineers who utilize modern tools of stochastic analysis.