|When:||Tuesday, Thursday 2:30 - 3:45|
|Where:||24 Hillhouse, main classroom|
|Office hours:||Initially, immediately after each lecture. More times to be added if needed.|
|Problem session:||To be arranged if needed|
|Other:||courses taught by DP in previous years|
|Short description:||Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis is assumed.|
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, plus a rewrite of section 2.11 (replacing cones by vector spaces). Ignore old 2.11.
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 follows the
The final grade will be based entirely on the weekly homework, which is due each Thursday.
Students who wish to work in teams (no more than 2 to a team) should submit a single solution set. Each member 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. Teams are expected to work independently of each other.