STAT 522: Advanced Theory of Probability

Winter Quarter 2004

Syllabus (last updated: 12/6/2004)

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: Denny 217

Prerequisites:

• Math/Stat 521 for 522.
• An interest in probability theory.

Required Texts:

• Probability for Statisticians by Galen R. 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. (1989). Real Analysis and Probability.
• 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. Foundationis of Modern Probability.
• Lo\'eve, M., Probability Theory, I and II.
• Pollard, D. A Users Guide to Measure Theoretic Probability.
• 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 (take home and in-class): 35%  
  In class part scheduled for Wednesday, March 17, 2:30 - 4:20 PM

Lectures:

The lectures in 522 will cover parts of Shorack's Chapters 10 - 18; the roughly equivalent material in Kallenberg is Chapters 3-6, 11- 13.

• Chapter 10. WLLN, SLLN, LIL, and Series
• Chapter 11. Convergence in Distribution
• Chapter 13. Characteristic Functions
• Chapter 14. CLT's via Characteristic Functions
• Chapter 15. Infinitely Divisible and Stable Distributions
• Chapter 8. Independence and Conditional Distributions
• Chapter 18. Martingales

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