## STAT 205B: Probability Theory (Spring 2008)

**Instructor** Elchanan
Mossel

**Teaching Assistant** Partha Dey

** Class time** 9:30-11:00 on TuTh at 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.

The course will cover

- Extra (than 205A) aspects of martingales.
- Markov Chains and Random Walks.

- Ergodic theory and applications.

- Brownian motions.

- Other topics.

Much of the material is covered in Chapters 5, 6, 7 in Durrett's
book, *Probability: Theory and Examples (3rd Edition)*
which is the required text. Quite a few of the homework problems are
from there
(note: 3rd edition).

Students who are intrested in more advenced reading are encouraged to
consult the
comprehensive book by Kallenberg, *Foundations of Modern Probability*.

For other relevant books, see Aldous list
at the old course homepage.

## Prerequisites

- 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 and function
spaces.

## Useful Links

- STAT 205 home
page by Jim Pitman - contains plenty of information / scribe notes etc.
from 205A & 205B taught over the years.

- STAT
205B Spring 2006 by David Aldous.

## Final

There will be a take-home final exam: assigned Thursday May 8, due
Tuesday May 13.
**Grading** 60% homework, 40% take-home final.

## Office Hours

Elchanan Mossel (mossel@stat)
Wednesdays 9-11 at 423 Evans
**TA **Partha Dey (partha@stat) Tue, 1-3pm at 387 Evans

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