MATH 275C: Spring 2025

MATH 275C: Spring 2025

Graduate Probability

lecturer: Marek Biskup
time and place: MWF 10-11 in MS 6627
make-up lectures: T 11-noon in MS 6201
office hours: 11-noon (after class)

Scheduling:

The first class (Monday, March 31) will be taught over zoom (link to be distributed by email); we will continue in-person from Wednesday, Apr 2. Due to conference travel, the classes on May 16, 19, 21, 23 and Jun 6 will have to be rescheduled or taught over zoom. Details to be settled during the first week of classes.

Lecture summary, board photos & notes: see here

Homework assignments:

HW#1 HW#2 HW#3 HW#4 HW#5 HW#6

General information:

Synopsis: This is the 3rd quarter of the 3+1-quarter UCLA Graduate Probability sequence. We will continue in the material treated in MATH 275A (taught by Jun Yin) and MATH 275B. We will proceed, roughly, according to the following plan:

Finishing ergodic theory started in 275B
Discrete-time Markov chains, random walks
Continuous-time processes: Renewal process, Markov chains
Processes with independent increments: Brownian motion, Lévy process
Markov processes

The prerequisites include good command of the material treated in previous quarters. This includes measure-based setup of probability theory, independent random variables and martingales. The course builds up towards MATH 275D (taught in Fall 2025) whose focus is on stochastic calculus.

Literature & resources:

Material will be drawn from the following textbooks:

R. Durrett, Probability: Theory and Examples, Cambridge Univ. Press.
T.M. Liggett, Continuous time Markov processes, Amer. Math. Soc.

Course credit:

To receive a successful grade, the student should be able to demonstrate sound knowledge of the specific material treated in the course which includes both a good handle of the theory and the ability to solve specific problems. The student's progress towards this goal will be checked by way of regular homework assignments during the quarter and a take-home final at the end thereof.