** Professor: **
Professor R. J. Williams

** Email: ** williams@math.ucsd.edu.

** Office: ** AP&M 6121.

** Office hours: ** M 4-5 p.m., W 1-2 p.m., and by appointment.

** Lecture time: ** 2-3.20 p.m.

There will be no lectures on Monday, April 19
or Wednesday, May 19, 2004.
There will be make-up lectures at another time.

** Place: ** AP&M 6438.

**
DESCRIPTION: **
Math 280ABC is the fundamental graduate probability sequence.
It covers measure theoretic probability essential for the pursuit
of research in probability or in fields in which probability is used in
applications.
Topics to be covered include:

1. Measure and integration from a probabilistic perspective.

2. Basic probabilistic notions of random variables,
expectation, independence.

3. Limit theorems:
laws of large numbers, convergence in distribution,
central limit theorems.

4. Martingale theory: conditional expectation,
convergence theorems, optional stopping.

5. Stochastic processes: a selection from random walk,
Markov chains, Brownian motion, Markov processes, stable
processes, stochastic integration.

Topics 1, 2, and part of 3 will be covered in Math 280A. The remainder of topic 3, and topics 4 and 5 will be covered in the subsequent two quarters of Math 280B, C. The text below will be supplemented with extra material for some topics such as Brownian motion.

** RECOMMENDED READING: **
Kai Lai Chung, Lectures from Markov processes to Brownian motion,
Springer.

** HOMEWORK FOR MATH 280C: ** Given out in class.

Please direct any questions to
Professor Ruth J. Williams, email:
williams@math.ucsd.edu

Last updated March 28, 2004.