STAT 205B Home Page

New: final homework assigned.

NEW:Take-home final exam: will be given out at end of last class (Thursday May 7), due 11.00am Tuesday May 12.

STAT 205B: Probability Theory (Spring 2009)

Instructor David Aldous

Teaching Assistant Ying Xu.

Class time TuTh 9.30 - 11.00 in room 330 Evans.

This is the second half of a year course in mathematical probability at the measure-theoretic level. It is designed for students whose ultimate research will involve rigorous proofs in mathematical probability. It is aimed at Ph.D. students in the Statistics and Mathematics Depts, but is also taken by Ph.D. students in Computer Science, Electrical Engineering, Business and Economics who expect their thesis work to involve probability.

In brief, the course will cover

Countable state Markov chains. Some old lecture notes. The Diaconis-Freedman Iterated random functions paper.
Extra (than 205A) aspects of martingales
(A little) large deviation theory
(A little) ergodic theory
Brownian motion: for more see the book Brownian motion by Peter Morters and Yuval Peres.

This roughly coincides with Chapters 5, 6, 7 in Durrett's book. See week-by-week schedule for more details. and for the weekly homework assignments.

Prerequisites

Ideally

STAT 205A - familiarity with measure-theoretic approach to mathematical probability.
Undergraduate-level familiarity with Markov chains.
Upper division analysis, e.g. uniform convergence of functions, basics of complex numbers. Basic properties of metric spaces helpful.

Books

R. Durrett Probability: Theory and Examples (3rd Edition) is the required text, and the single most relevant text for the whole year's course. Most of the homework problems are from there (note: 3rd edition). The style is deliberately concise.

There are many other books at roughly the same ``first year graduate" level. Here are my personal comments on some.

P. Billingsley Probability and Measure (3rd Edition) Chapters 25-30 make a nice treatment of the "convergence in distribution" part of 205A.

Y.S. Chow and H. Teicher Probability Theory. Uninspired exposition, but has useful variations on technical topics such as inequalities for sums and for martingales.

R.M. Dudley Real Analysis and Probability. Best account of the functional analysis and metric space background relevant for research in theoretical probability.

B. Fristedt and L. Gray A Modern Approach to Probability Theory. 700 pages allow coverage of broad range of topics in probability and stochastic processes.

L. Breiman Probability. Classical; concise and broad coverage.

Final

There will be a take-home final exam: see dates at top of page.

Grading 70% homework, 30% take-home final.

Office Hours

David Aldous (aldous@stat) Wednesdays 9.30-11.30 in 351 Evans

Ying Xu (yingxu@stat) Mondays 3.00 - 4.00 and Wednesdays 2.30 - 3.30 in 387 Evans.

If you email us, please put STAT 205B in subject.