Math/Stat 832 - Theory of Probability

Spring 2011

Meetings: TR 11-12:15, VAN VLECK B131
Instructor: Benedek Valkó
Office: 409 Van Vleck
Phone: 263-2782
Email: valko at math dot wisc dot edu
Office hours: TR 9:30-10:30 or by appointment
Grader: Diane Holcomb

I will use the class email list to send out corrections, announcements, please check your email from time to time.

Course description:
This is the second semester of an introductory course on graduate level mathematical probability theory. 832 covers core topics in discrete-time and continuous-time stochastic processes. This includes martingales, Markov chains, point processes, stationary processes and ergodic theory, Brownian motion, and diffusion processes.

Textbook: Richard Durrett: Probability: Theory and Examples

There are several good textbooks on probability and it might help to have a look around. An excellent reference book (which was actually used as the textbook for 831-832 recently) is:
Olav Kallenberg: Foundations of Modern Probability.

Prerequisites: Basic knowledge of measure theory and comfort with rigorous analysis is important for this course. We will rely on the theory introduced in the first semester of the course, so a review of the basic notions and definitions might be useful.

Course Content: we will cover (at least) the following topics (mostly contained in chapters 6-8 of Durrett):

Evaluation: Course grades will be based on home work assignments, a take-home final exam at the end of the semester.

Extra notes on the martingale central limit theorem (based on notes of S. Sethuraman).


Instructions for the homework assignments:
Homework must be handed in by the due date, either in class or by 12PM in the instructor's mailbox. Late submissions will not be accepted. Group work is encouraged, but you have to write up your own solution.
You can use basic facts from analysis and measure theory and also the results we cover in class. If you use other literature for help, cite your sources properly. (Although you should always try to solve the problems on your own before seeking out other resources.)