Statistics 330/600 (Spring 2008)

Advanced Probability

Instructor: David Pollard
When: Tuesday, Thursday 2:30 - 3:45
Where: 113 WLH
Office hours: after each class
TA:Wei Dou
Problem session:to be arranged if needed

Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.

Intended audience

The course is aimed at students (both graduate and undergraduate) who are either comfortable with real analysis or who are prepared to invest some extra effort to learn more real analysis during the course. Prior exposure to an introductory probability course (such as Stat 241/541) would be an advantage, but is not essential.

Knowledge of measure theory is not assumed. The first two weeks of the course will introduce key measure theoretic ideas, with other ideas explained as needed.


Pollard, User's Guide to Measure Theoretic Probability
Cambridge University Press 2001. A sample: UGMTP-extract = first two chapters from UGMTP.

If you prefer a more standard text, one of the books on the list of references might be to your taste.


Coverage similar to the description at the end of the Preface, which is included in UGMTP-extract.


The final grade will be based entirely on the weekly homework.

Students who wish to work in teams (no more than 2 to a team) should submit a single a solution set. All members of a team will be expected to understand the team's solutions sufficiently well to explain the reasoning at the blackboard. Occasional meetings with DP will be arranged.

DBP 12 Jan 2008