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)
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.
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
Evaluation
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.
Piazza
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.