STAT 522: Advanced Theory of Probability

Winter Quarter 2008: Syllabus (last updated 12/7/2007)

Course personnel:

• Professor: Jon A. Wellner
• B320 Padelford Hall
• Phone: 543-6207
• Office hours: 1:30 - 3:30 MWF; or by appointment

Administrative Information:

• Time(s): MWF 11:30 - 12:20
  
• Place: MEB 251
• I will be absent on during the first week of classes, January 7, 9, and 11. Lectures will be given by Marios Pavlides on those dates. He will cover the material in section 10.7 plus some additonal material on weak laws of large numbers and the St. Petersburg paradox.

Prerequisites:

• Mathematical Analysis at the level of Math 424-5-6.
• An interest in probability theory.
• Math/Stat 521

Required Texts:

• Probability for Statisticians, by Galen Shorack, 2000. Required.

Supplemental probability texts:

• Billingsley, P., (1986). Probability and Measure.
• Breiman, L., (1968). Probability.
• Chow, Y.S., and Teicher, H. (1978). Probability Theory.
• Chung, K. L., (1974). A Course in Probability Theory.
• Dudley, R. M. (2002). Real Analysis and Probability.
• Durrett, R. (1991). Probability: Theory and Examples.
• Feller, W. (1957). An Introduction to Probability Theory and Its Applications, Volume I.
• Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Volume II.
• Kallenberg, O. (1997). Foundations of Modern Probability
• Lo\'eve, M., Probability Theory, I and II.
• Williams, D, Probability with Martingales.

Supplemental analysis and measure theory texts:

• Bartle, R. G. (1966). The Elements of Integration.
• Cohn, D. (1980). Measure Theory.
• Royden, H. L. (1963). Real Analysis.
• Rudin, W. (1964). Principles of Mathematical Analysis.

Grading:

• Homework: 35%
• Midterm: 30%
• Final: 35%
  (Scheduled time & date: 2:30 - 4:20, Wednesday, March 19, 2:30 - 4:20

Lectures:

• Chapter 8. Sections 8.4 - 8.6.
• Chapter 11. Convergence in distribution
• Chapter 13. Characteristic functions
• Chapter 14. CLT's via characteristic functions
• Chapter 15. Infinitely divisible and stable distributions
• Chapter 12. Brownian motion and empirical processes.

Click here to return to Jon Wellner's home page.

Click here to return to the Statistics Dept. home page.

Click here to return to the University of Washington home page.