Synopsis for Stochastic Differential Equations

Construction of Brownian motion, continuous time martingales. It^os calculus: stochas- tic integrals with respect to martingales, It^os formula, Levy's theorem on characterizing Brownian motion, exponential martingales, Girsanov's theorem, the martingale representa- tion theorem. Stochastic dierential equations: strong solutions, questions of existence and uniqueness, diusion processes, Cameron-Martin formula, weak solutions and martingale problems. Some selected applications chosen from option pricing, stochastic ltering etc.

(Prof Ben Hambly - 16 lectures - MT - Core course)
Stochastic dierential equations have been used extensively in many areas of application, including nance and social science as well as Chemistry. This course develops the basic theory of Itos calculus and stochastic dierential equations, and gives a few applications.