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: MW, 1-1.50 p.m.
Teaching Assistant: Michael Kelly, AP&M 6333.
TA Office hours: Tu, 2-3 p.m.

Lecture time: MW 5-6.30 p.m.
Place: AP&M 6402 (Please note change of room from earlier schedules).

Problem Session: Fridays, 3-3.50 p.m., AP&M 6402. The TA will hold a problem session each Friday at this time.

Midterm: There will be a midterm exam on Wednesday, November 17, 2010, in class. It will test the material covered in lectures and in related readings from the book through Wednesday, November 10 and in homework assignments 1-5. Please bring your student ID, a blue book or two, and pens/pencils to write with. No books or notes are allowed. You may not bring a calculator -- you will not need one. Make sure to justify your answers (credit will not be given for "inspired'' answers). Remember that part of each problem is to set it up and to arrive at the answer by a progression of logical steps. Please start each problem on a new page, write legibly, and put your name and section number on your blue book.
There will be an extra problem session on Tuesday, November 16, 4-5pm in AP&M 6402.

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: S. Resnick, A Probability Path, Birkhauser, Boston.

HOMEWORK: 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 May 10, 2010.