STAT 523: Advanced Theory of Probability
Spring Quarter 2020
Tentative Syllabus (last updated: 3/26/20)
Course personnel:
- Professor: Jon A. Wellner
- B320 Padelford Hall (home office)
- Phone: 543-6207, 206-747-0030
- Office hours: 1:30 - 3:30 MWF; or by appointment
Administrative Information:
- Time(s): MWF 11:30 - 12:20
- Place: MEB 251 (via Zoom )
- Jon W. unable to host lecture on 17 April (Friday) due to electricity shutdown
Makeup: 15 April (Wednesday) 11:00 AM to 11:30 (plus usual lecture 11:30-12:20)
and 22 April (Wednesday) 11:00 AM to 11:30 (plus usual lecture 11:30-12:20)
Prerequisites:
- Math/Stat 522 for 523.
- An interest in probability theory.
Required Texts:
-
Probability for Statisticians,
by G. R. Shorack, 1998; 2017
-
Probability: Theory and Examples, 5th Edition, by R. Durrett (2019).
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 8 May.
- Project: 35%, Due Monday, June 8; Tentative outline due Monday, May 4
(See Course Project Handout)
-
Course Evalution
(https://uw.iasystem.org/survey/224826 )
Lectures (tentative plan):
- The strong Markov property: PfS Sections 8.7 and 12.5
- Embeddings in Brownian motion: PfS Sections 12.6 and 12.8
- Brownian motion, continued: PfS Section 12.9
- CLT's via Characteristic functions: PfS Section 10.0 - 10.5
- CLT via Stein's method: Chen, Goldstein, and Shao
- Infinitely divisible and stable distributions: PfS, Chapter 11
- Stochastic calculus: from Chung and Williams, McKean, and Durrett
Recording of the lectures
This course is scheduled to run synchronously at the scheduled
class time via Zoom. These Zoom class sessions will be recorded.
The recording will capture the presenter’s audio, video and
computer screen. Student audio and video will be recorded
if they share their computer audio and video during the
recorded session. The recordings will only be accessible
to students enrolled in the course to review materials.
These recordings will not be shared with or accessible to the public.
The University and Zoom have FERPA-compliant agreements in place
to protect the security and privacy of UW Zoom accounts.
Students who do not wish to be recorded should:
- Change their Zoom screen name to hide any personal identifying
information such as their name or UW Net ID, and
- Not share their computer audio or video during their Zoom sessions.
Click here to return to the 523 web page.
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