Cornell Math - MATH 778 Spring 2007

MATH 778: Stochastic Processes (Spring 2007)

Instructor: Soumik Pal

Meeting Time & Room

The course objective is to cover a wide variety of topics in continuous stochastic processes which depend on stochastic calculus and have gained importance in probability or other areas in mathematics. First we will create our toolbox: review of Ito calculus, martingales, and introduce local times and some widely applicable results . Then we will use them to analyse the following.

1. Interplay between probability and differential equations, particularly the heat and Feynman-Kac equations.
2. Markov processes.
3. Some path properties of Brownian motion including occupation time measures.
4. Other fundamental processes: Brownian bridge, Ornstein-Uhlenbeck and the Bessel processes.

On our way we will encounter some of the fascinating, deep theorems of modern probability.

Course Outline