STAT 521: Advanced Theory of Probability

Fall Quarter 1998

Syllabus (last updated: 9/20/98)

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: Parrington 212

Prerequisites:

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

Required Texts:

• Foundations of Modern Probability, by Olav Kallenberg, 1998. Required.
• Probability for Statisticians, by G. R. Shorack, 1998 (will be handed out as the course progresses).

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.
• 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.
• \item 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, Tuesday, December 15).

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

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