Math 672 — Probability Theory

Spring 2003

Instructor: Rick Durrett

Time: TR 1:25-2:40

Room: MT 206

This course is the continuation of Math 671 and covers Chapters 4-7 of my book Probability: Theory and Examples. The main topics are

4. Martingale theory. These processes in which the state at time n+1 is on the average the position at time n, have a rich theory that is useful in a number of contexts.

5. Markov chains. This subject can be taught at the Master's or undergraduate level but is more fun when you can use martingale theory and other more sophisticated tools to do the proofs.

6. Ergodic theory. The main result here is Birkhoff's ergodic theory, a generalization of the law of large number that does not require independence but only stationarity (translation invariance of the joint distribution).

7. Brownian motion. We will investigate its Markov and martingale properties and show that it arises as a limit of sums of independent random variables.

Last modified: April 7, 2003