Math 562, Theory of Probability II

Prerequisite: Math 561

Textbook used in recent years:

• Jean-Francois Le Gall: Brownian Motion, Martingales, and Stochastic Calculus Springer, 2016.
• Karatzas and S. Shreve: Brownian Motion and Stochastic Calculus, 2nd Edition, 1994, Springer.

1. Brownian motions, continuous time martingales, local martingales, semimartingales

2. Stochastic integrals, Ito’s formula, Girsanov theorem, martingale representation theorem

3. Stochastic differential equations, strong solutions, weak solutions, martingale problems

4. Connections with partial differential equations