Statistics 330/600 (Spring 2007)
Advanced Probability
Instructor:

David Pollard

When:

Tuesday, Thursday 2:30  3:45

Where:

113 WLH

Office hours:

after each class

TA:  Xi Luo 
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.
Text
Pollard, User's Guide to Measure Theoretic Probability
Cambridge University Press 2001. A sample:
UGMTPextract = 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.
Topics
Coverage similar to the description at the end of the
Preface, which is included in
UGMTPextract.
Grades
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.

Homework due each Thursday
 Handouts, including some extracts from
UGMTP and rewrites of UGMTP.

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 13 Jan 2007