Statistics 330/600

Advanced Probability

Instructor: David Pollard
When: Tuesday, Thursday 2:30 - 3:45
Where: 24 Hillhouse Avenue (Statistics Department)
Office hours: Wednesday 1:00-3:00; and after lectures on Tuesday and Thursday (more hours to be arranged if necessary)

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 measure theoretic ideas (sigma-fields, countable additivity, integrals, monotone convergence, dominated convergence, generating classes--compare with the chapter Modicum.pdf from spring 99). Other measure theoretic ideas will be introduced during the course, as needed.


I will be revising the notes from spring 99, in preparation for publication by the end of the semester. Yale students will have free access to the notes (in Acrobat pdf format) as they are revised. If you choose to learn from the notes, you will have the advantage of working from the material on which the lectures are based. You will have the disadvantage of receiving new versions in installments, only shortly in advance of lectures. Also the notes have no index yet. (Preparation of an index is one of the final tasks before publication.)

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


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.

Current versions of notes


Class materials from spring 99 (with additions).

EMAIL: questions and answers regarding problem sets, notes, and anything else related to the course.

Class materials for an introductory probability course (Stat 241/541, Fall 97), containing more extensive elementary discussion of probabilistic ideas. See, in particular, the Chapters 2 and 5, on conditional expectations and on symmetry.

DBP 16 Jan 2000