Statistics 330/600 (Spring 2004)

Advanced Probability

Instructor: David Pollard
Email: david.pollard@yale.edu
When: Tuesday, Thursday 2:30 - 3:45
Where: Luce 202 (34 Hillhouse Ave)
Office hours: after class, outside 202 Luce
TA:Xiaoxian Luo

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.

Text

Pollard, User's Guide to Measure Theoretic Probability
Cambridge University Press 2001. [Table of contents]

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

Topics

Coverage similar to the description at the end of the Preface.

Grades

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

Students who wish to work in teams (no more than 3 to a team) should submit a single a solution set, which will be discussed during a weekly meeting with DP. All members of a team will be expected to understand the team's solutions sufficiently well to explain the reasoning at the blackboard.

Homework

Handouts

Class materials for an introductory probability course (Stat 241/541, Fall 2000), containing more extensive elementary discussion of probabilistic ideas. See, in particular, the Chapters 2 and 4, on conditional expectations and on symmetry.


DBP 18 Jan 2004