Math 275B: Probability Theory

Winter 2012


Math 275 is an introduction to rigorous probability at the graduate level. The Winter quarter will give an introduction to stochastic processes in both discrete and continuous time, including: martingales; stationary processes; and brownian motion.

While you may have encountered some of these topics in an undergraduate probability course, we will take a much deeper look at them here. This course follows (and requires the equivalent of) Math 275A (Fall 2011) and will be followed by (and required for) Math 275C (Spring 2012) which will develop further the theory of stochastic processes in continuous time with an emphasis on Markov processes. It should appeal both to students interested in pure mathematics (esp. analysis) and in applications (esp. physics, engineering, biology, economics).

Prerequisites: Math 275A or equivalent.

General Information


Lecture Notes

UPDATE [Sep 1, 2015]: The latest version of the lecture notes can be accessed here.

The following lecture notes are strongly influenced by the references above. They have not been proofread very carefully, so use them at your own risk. A file containing all the notes is here.


Last updated: March 20, 2012.