University of Connecticut

Course Info

MATH 5016: Topics in Probability

Description: Advanced topics in probability theory, theory of random processes, mathematical statistics, and related fields. With a change of content, this course is repeatable to a maximum of twelve credits.

Credits: 3

MATH 5016 - Section 1: Topics in Probability

Description: Advanced topics in stochastic processes: applications to PDE and integro-differential equations This course will include many of the following topics:

  1. Stochastic differential equations
  2. Representing the solutions of PDE by means of diffusions
  3. Martingale problems - the uniqueness theory of Stroock and Varadhan
  4. Harnack inequalities - the methods of Krylov-Safonov
  5. Heat kernel estimates
  6. Jump processes and their stochastic calculus
  7. Harnack inequalities for integro-differential operators
  8. Potential theory for the fractional Laplacian
The material will be similar to what is covered in my lecture notes on my web page; see "PDE from a probability point of view" and "Lecture notes for the Cornell Summer School in Probability 2007."

Offered: Fall

Credits: 3

Sections: Fall 2008 on Storrs Campus

Course Sec Comp Time Room Instructor
5016 001 Lecture TuTh 12:30-01:45 MSB319 Bass, Richard