Mathematics 706 - Stochastic Calculus

This course provides an introduction to the theory of stochastic differential equations oriented towards topics useful in applications (Brownian motion, stochastic integrals, and diffusion as solutions of stochastic differential equations), and the study of diffusion in general (forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus, as well as Girsanov's theorem, Feynman-Kac formula, Martingale representation theorem). Applications to mathematical finance will be included as time permits.