Stochastic Calculus

This course is an introduction to stochastic calculus for continuous processes. The main topics covered are: construction of Brownian motion, continuous time martingales, Ito integral, localization, Ito calculus, stochastic differential equations. Girsanov theorem, martingale representation, Feynman-Kac formula. If time permits, a brief introduction to stochastic control will be given.