734Math/Stat  - Theory of Probability II

Spring 2022

Meeting times: Tuesdays and Thursdays, 1:00PM - 2:15PM
Meeting place: Van Vleck B135.
Instructor: David Anderson
Office: 617 Van Vleck
Instructor E-mail: anderson@math.wisc.edu
Office hours: 11am-12pm on Monday and 10am-11am on Tuesdays.   I will have my office hours via Zoom for the time being.

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 (This is available for free from his website: https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf)


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 - 7 of Durrett.  This is a rough outline of the course:

Weeks 1-3: Martingales (review,
Doob's inequality, uniform integrability, backwards martingales)
Weeks 4-8: Markov chains

Weeks 9-10: ergodicity, subadditive ergodic theorem
Week 11: Poisson processes (Section 3.7 plus extra material)
Weeks 12-14: Brownian Motion


Course grades will be based on biweekly home work assignments (40%), a midterm exam (30%) and the final exam (30%). (See the Canvas page for more information.)

These are the scheduled times for the exams:
Midterm exam: Wednesday, March 9th, 7:30pm-9:30pm. Location: Van Vleck B239.
Final Exam: Sunday, May 8th, 10:05am - 12:05am.  Location: Mechanical Engineering 2121.


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 team@piazza.com.
You can access our Piazza page from the Canvas page of the course.

Instructions for homework assignments