STAT 523: Advanced Theory of Probability

Spring Quarter 2013

Tentative Syllabus (last updated: 4/1/13)

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 C-301
• Jon W. away May 29-31; make-up lectures 4/17 Wednesday (9:30-10:30 AM)
  5/1 Wednesday (9:30-10:30 AM), Padelford C301.

Prerequisites:

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

Required Texts:

• Probability for Statisticians, by G. R. Shorack, 1998

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 10 May.
• Final: 35%
  (Scheduled time & date: 2:30 - 4:20 PM, Wednesday, June 12

Lectures:

The tentative plan for lectures in 523 is to cover Shorack's Chapters 10-12, followed by more of JW's chapter 11 and further material on stochastic processes, including martingale CLT and stochastic integration

• Chapter 10: central limit theorems via characteristic functions
• Chapter 11: Infinitely divisible and stable distributions.
• Chapter 12: Brownian motion, embedding, and empirical processes.
• JW Chapter 11 notes, section 4-5.
• Stochastic calculus: from Chung and Williams, McKean, and Durrett
• Further material on entropy driven clt's as time permits

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

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

Click here to return to the University of Washington home page.