STAT 521: Advanced Theory of Probability

Fall Quarter 2019: Syllabus (last updated 08/14/2019)

Course personnel:

• Professor: Jon A. Wellner
• B320 Padelford Hall
• Phone: 543-6207
• Office hours:
  1:30 - 3:30 MF;
  8:30 - 10:00 Tuesday (CSSS conference room);
  or by appointment.

Administrative Information:

• Time(s): MWF 11:30 - 12:20
  
• Place: Low 106
• I will be absent on Wednesday, September 25.
  Make up for the missed lecture on 25 September.
  Friday 25 October from 8:30 - 9:20 AM, Low 101
  

Prerequisites:

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

Required Texts:

• Probability: Theory and Examples, 5th edition, by Rick Durrett, 2019. Required.
• Probability for Statisticians, by Galen Shorack. Online version from 2012. Recommended.

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.
• 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% (November 1, 2019)
• Final: 35%
  (Scheduled time & date: Wednesday, December 11, 2019, 2:30 - 4:20 PM)

Lectures:

• Chapter 1. Measures
• Chapter 2. Measurable Functions and Convergence
• Chapter 3. Integration
• Chapter 4. Derivatives via signed measures
• Chapter 5. Measures and Processes on Products
• Chapter 8. Independence and Conditional Distributions
• Chapter 9. Special Distributions
• Chapter 10. WLLN, SLLN, LIL, and Series

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

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

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