BOOKS
The required text for Math 280ABC is the SECOND edition of the book Probability: Theory and Examples by Richard Durrett, Duxbury Press, 1995. For Math 280C, the book Introduction to Stochastic Integration by K. L. Chung and R. J. Williams, Birkhauser, Boston, 1990, is a recommended reference.

PREREQUISITES AND COMPLEMENTARY COURSES
A knowledge of undergraduate real analysis, such as found in Rudin's Principles of Mathematical Analysis is recommended. Students who have not had a graduate course in Measure Theory may want to consider attending the first quarter of Math 240A, Real Analysis, taught by Professor Driver.

The undergraduate probability courses, Math 180ABC, especially Math 180BC, are complementary to Math 280. Math 180A is an introduction to the basic concepts of probability, without measure theory. Math 180BC provide a good introduction to some basic stochastic processes used in modelling such as random walk, Poisson process, Markov chains.

In the Spring of 1996, Professor Williams will be teaching a Topics in Probability course (Math 289A), for which Math 280AB/C is an advised pre/co-requisite.

TOPICS FOR 280ABC
1. Review of measure and integration from a probabilistic perspective.
2. Basic notions: random variables, expectation, independence.
3. Limit theorems: laws of large numbers, central limit theorems.
4. Martingale theory: conditional expectation, convergence theorems, optional stopping.
5. Random walk and Brownian motion.
6. Stochastic integration.
7. Stochastic processes: a selection from point processes, Markov chains, Markov processes, stable processes.