Mathematics 797P - ST- Stochastic Calculus

We first review some basic probability and useful tools, including random walk, Law of large numbers and central limit theorem. Conditional expectation and martingales. The topics of the course include the theory of stochastic differential equations oriented towards topics useful in applications, such as Brownian motion, stochastic integrals, and diffusion as solutions of stochastic differential equations. Then we study about 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. We will also include some applications to mathematical finance as time permits.

Open to Graduate students only. STATISTC 605