Instructor: Allanus Tsoi

Description: My purpose for offering this course is to help the students to build up a rather solid foundation about the theory of Markov processes, so that they will have the necessary tools to understand the interaction between the theory of Markov Processes and classical potential theory (in Doob's sense) in the future. This course begins with a discussion of the Markov property, the transition functions, semigroups, and some measurability theories. Then we will look into the martingale connection and Feller processes. In the second half of the semester we will concentrate on Hunt processes and discuss its relation with the concept of "balayage" (sweeping out) in potential theory.

Textbook: Lecture from Markov Processes to Brownian Motion - by Kai Lai Chung. (Springer) (Hopefully I can finish at least Chapter 1, 2, and 3)

Prerequisite: a graduate course in measure theory. (math 8420).