Discrete and continuous time martingales, Brownian motion, stopping times, martingale convergence theorems, local martingales and semimartingales, predictable and optional processes, the It么 stochastic integral, quadratic and mutual variation, the It么 formula, representations of martingales, local times, Girsanov theorem, stochastic differential equations and applications, Stratonovich integration. Three term hours; lectures. (3.0 credit units).
Discrete and continuous time martingales, Brownian motion, stopping times, martingale convergence theorems, local martingales and semimartingales, predictable and optional processes, the It么 stochastic integral, quadratic and mutual variation, the It么 formula, representations of martingales, local times, Girsanov theorem, stochastic differential equations and applications, Stratonovich integration. Three term hours; lectures. (3.0 credit units).
