Cornell Math - MATH 778, Spring 1999

MATH 778 — Spring 1999
Markov Processes: Selected Topics

Instructor: E. B. Dynkin

Time:  TR 10:10-11:25

Room: WE 328

Some directions of recent research in theory of Markov processes will be discussed including:
 

1. Boundary theory of Markov processes (Martin boundaries; the behavior of paths at the boundary; boundary value problems for partial differential equations).
    

2. Markov processes as a tool in field theory (Gaussian and non-Gaussian random fields associated with Markov processes; applications to quantum field theory and to investigating local times of a Markov process).
    

3. Additive functionals and related transformations of Markov processes (killing and mass creation; random time change; Girsanov's transformation).

I shall try to avoid generalities and technicalities and to emphasize ideas illustrated on concrete examples.