STAT 523: Advanced Theory of Probability

Spring Quarter 2017

Tentative Syllabus (last updated: 3/9/17)

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: Padelford CMU-228
• Jon W. away May 12, May 31, and June 2; make-up lectures TBA
  4/19 and 4/26 Wednesday 12:30 - 1:20, CMU 230.

Prerequisites:

• Math/Stat 522 for 523.
• An interest in probability theory.

Required Texts:

• Probability for Statisticians, by G. R. Shorack, 1998;
  
• Probability: Theory and Examples, 4th Edition, by R. Durrett (1951).
  

Recommended Text:

• Normal Approximation by Stein's Method by L.H.Y. Chen, L. Goldstein, and Qi-Man Shao (2011).

Supplemental texts:

• Billingsley, P., (1986). Probability and Measure.
• Billingsley, P., (1999). Convergence of Probability Measures, Second Edition.
• 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.
• Lo\'eve, M., Probability Theory, I and II.
• Chung, K.L. and Williams, R. Introduction to Stochastic Integration
• McKean, H.P. (1969). Stochastic Integrals

Grading:

• Homework: 35%; handed out on Wednesday, due following Wednesday.
• Midterm: 30%, Friday 12 May.
• Project: 35%, Due Monday, June 5; Tentative outline due Wednesday, May 3
  

Lectures:

The tentative plan for lectures in 523 is to cover Shorack's Chapters 9-12, followed by Stein's method and further material on Brownian motion and stochastic processes, including martingale CLT and stochastic integration

• Chapter 9: characteristic functions
• Chapter 10: central limit theorems via characteristic functions
• Chapter 11: infinitely divisible and stable distributions.
• Stein's method: an introduction.
• Chapter 12: Brownian motion, embedding, and empirical processes.
• Stochastic calculus: from Chung and Williams, McKean, and Durrett

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

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

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