STAT 522: Advanced Theory of Probability

Winter Quarter 2020: Syllabus (last updated 1/31/2020)

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 January 27, 29, and 31. Makeup lectures have been scheduled as follows:
  Make-up lecture 1: 7 February (Friday), 9:30 - 10:20 AM, SIG 226
  Make-up lecture 2: 24 February (Monday), 9:30 - 10:20 AM, SIG 226
  Make-up lecture 3: 2 March (Monday, 9:30 - 10:20 AM, SIG 226
  

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 G. R. Shorack. (2000). Online version from 2012. Required
• Stochastic Processes, by Richard Bass. 2011. Required.
• Probability: Theory and Examples , by Rick Durrett, 2010; 4th edition. 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.
• 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.

Reviews of Recent Books on Statistics and Probability:

• David Aldous's reviews

Grading:

• Homework: 35%
• Midterm: 30%; Friday, February 14 (during the usual class time)
• Final: 35%
  (Scheduled time & date: 2:30 - 4:20, Wednesday, March 18.

Lectures:

• Chapter 8. Sections 8.4 - 8.6.
• Chapter 7. Sections 7.4 and 7.5, Conditional Expectations
• 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.

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