Math/Stat 734 - Theory of Probability II.

Spring 2021

Meetings: TR 1pm-2:15pm (online)
Instructor: Benedek Valkó
Email: valko at math dot wisc dot edu
Office hours: To be announced (see Canvas page)

This page gives an overview of the course, all relevant information and resources will be provided in the official Canvas page.

Course description

This is the second semester of an introductory course on graduate level mathematical probability theory. 734 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.


Richard Durrett: Probability: Theory and Examples, 5th edition, 2019

There are several good textbooks on probability and it might help to have a look around. Here is a list of textbooks that could be used for extra reading:


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 cover selected portions of Chapters 4-8 of Durrett. This is a rough course outline:

Weeks 1-2: Martingales (review, Doob's inequality, uniform integrability, backwards martingales)
Weeks 3-7: Markov chains
Weeks 8-9: Stationary sequences, ergodicity, subadditive ergodic theorem
Weeks 10-14: Brownian motion


Course grades will be based on biweekly home work assignments (25%), class participation (15%), a midterm exam (30%) and the final exam (30%). (See the Canvas page for more information.)


We will be using Piazza for class discussion.  The system is catered to getting you help fast and efficiently from classmates and myself.  Rather than emailing all questions to me, I encourage you to post your questions on Piazza. If you have any problems or feedback for the developers, email
You can access our Piazza page from the Canvas page of the course.

Instructions for homework assignments

If you would like to learn more probability...

Check out the Probability Seminar, the Graduate Probability Seminar and the Statistics Seminar for talks that might interest you. Have a look at the wiki page of our probability group to learn more about the probabilists at UW-Madison.