## Mathematics 275: Probability Theory and Stochastic Processes

## Mathematics 275B - Winter 2009

**Time and place:** MWF at 1 in MS 6201
**Instructor:** Thomas M. Liggett
**Office hours:** MWF 2-2:30 in MS 7919
**TA:** Alexander Vandenberg-Rodes; his office hours are M 11-12 and W 12-1 in MS 6154.
**Text:** Probability: Theory and Examples, 3rd edition,
by R. Durrett
**Topics:** (a) Random Walks, (b) Martingales, (c) Additive
and Subadditive Ergodic Theory
**Grades** will be based on homework to be assigned from
Durrett's book. There will be 5 assignments. The last one will be
somewhat longer than the others, and is to be done with no consultation
(with the instructor, other students, or anyone else).

## Assignments

**Due January 21:** Section 3.1 #1.2, 1.4, 1.6, 1.7, 1.12, 1.14, 1.15
**Due February 4:** Section 4.1 #1.1,1.3,1.4,1.5,1.6 and problems B1,B2,B3 distributed in class.
**Due February 18:** Chapter 4 #1.10 (use conditional expectation and its properties), 1.11, 2.3, 2.4, 2.6, 2.9, 2.11
**Due March 4:** Chapter 4 #3.2,3.9.3.10.3.11(these three problems are based on Theorem 3.5, which you should read, since I will not cover it in class),4.5,4.7,4.8,4.9,4.10,7.1.
**Due March 13:** Final assignment; to be done without consultation.