Math 672 — Spring 2002 Probability Theory

This is a second semester of graduate probability.

The exact topics covered will depend somewhat on the topics covered in Math 671, but based on the preliminary description of Math 671, I expect to do the following:

• Discrete time Martingales
   
• Construction and properties of Brownian motion including relationship to solutions of partial differential equations.
   
• Introduction to stochastic integration and stochastic differential equations
   
• Stable processes and/or fractional Brownian motion (if time allows)

I will assume that students have seen measure theoretic probability, but I do not consider Math 671 to be a strict prerequisite.