**
MATH 280ABC: PROBABILITY (FALL 2010, WINTER 2011, SPRING 2011)
**

** Professor: **
Professor R. J. Williams, AP&M 6121.

** Email: ** williams at math dot ucsd dot edu.

** Office hours: ** M 2.10-3 pm, W 1-2 pm (except on Wed April 20,
the office hour will be at 4-4.45 pm).

** Teaching Assistant: ** Michael Kelly, AP&M 6333.

** TA Office hours: ** Tu 2-3pm.

** Lecture time: ** MW 5-6.30 p.m.

** Place: ** AP&M 5402.

** Problem Session: ** The TA will
hold a problem session. This will be at 3-3.50pm on
Fridays in AP&M 5829.

**
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, ergodic theory,
Markov chains, Brownian motion, Markov processes, stable
processes.

** TEXT FOR MATH 280AB: ** S. Resnick, A Probability Path, Birkhauser, Boston.

** REFERENCES FOR MATH 280C: **

K. L. Chung, Markov Processes, Brownian Motion and Time Symmetry,
Springer, 2005.
E. Cinlar,
Probability and Stochastics, Springer, 2011.
T. M. Liggett, Continuous Time Markov Processes, American Mathematical Society,
2010.

** HOMEWORK: ** For Math 280C homework, click here.
The assessment for Math 280C will be based on homework.

For Math 280B homework and the midterm, click here.

For Math 280A homework and the midterm, click here.

** OTHER REFERENCES: **

Krishna B. Athreya and Soumendra N. Lahiri,
Measure Theory and Probability Theory
Springer Texts in Statistics, 2006.
H. Bauer, Probability Theory and Elements of Measure Theory, Academic Press,
New York, 1981.
P. Billingsley, Probability and Measure, Wiley, New York.
L. Breiman, Probability, Addison-Wesley, 1968.
Y. S. Chow and H. Teicher, Probability theory, Springer, New York, 1988.
K. L. Chung, A Course in Probability Theory, Revised Edition, Academic Press, New York, 2000.
R. Dudley, Real Analysis and Probability, Cambridge University Press, 2002.
Rick Durrett, Probability,
Theory and Examples,
4th Edition,
Series: Cambridge Series in Statistical and Probabilistic Mathematics.
Allan Gut,
Probability: A Graduate Course
Springer Texts in Statistics, 2005.
Jean Jacod and Philip Protter, Probability Essentials, Springer, 1999.
A. N. Shiryayev, Probability, Springer-Verlag, New York, 1984.
Olav Kallenberg,
Foundations of Modern Probability,
Probability and its Applications, 1997.
David Pollard, A User's Guide to Measure Theoretic Probability,
Cambridge University Press, 2002.
David Williams, Probability with martingales, Cambridge
University Press, Cambridge, England, 1991.

Last updated October 10, 2011.