Math 551 - Advanced Probability I - Fall 2003

Probability theory based on measure theory. Strong law of large numbers, central limit theorem, martingales, applications of martingales.

Topics covered:

Review of measure theory;  expectation and independence;  weak and strong laws of large numbers;  Kolmogorov and Hewitt-Savage zero-one laws;  characteristic functions;  central limit theorems;  martingales;  applications of martingales;  Lindeberg-Feller theorem (if there is time).

Prerequisites:

Math 451 (Measure theory) or its equivalent. Math 451 can be taken concurrently with permission of instructor.

Textbook:

A Course in Probability Theory, 3rd edition.
Authors:  Kai Lai Chung (Academic Press, 2001).

Class Time and Location:

Tentative: MWF 3:00-4:00   --   Cupples I  Rm 199

Links:

Homework Assignments
Take-Home Final
Back to Prof. Sawyer's home page

Professor:

Prof. S. Sawyer   --   Cupples I  Room 107
Phone: (314) 935-6703
Email:  sawyer@math.wustl.edu

Office Hours:

TTh 3:00-4:00pm    Office:  Rm 107 Cupples I

Exams, Homework Sets, and Grades:

There will be around five homework sets and a takehome final. There may be an in-class oral presentation. Grades will be based on on the homework sets (around 60%) and the final and oral presentation (around 40%). Cr means D or better if you elect ``Credit/No Credit.''

Collaboration:

Collaboration on homework is allowed and can be helpful (and fun). Collaboration on homework is encouraged. However, you must do all written work by yourself.
If you collaborate with someone on a homework, you must list his or her name in a note at the top of the first part of your homework.

Collaboration on Takehome Tests:

There should be NO COLLABORATION on takehome tests.

WARNING:

Make a copy of each homework before you hand it in !!
It may not be returned before you need to refer to it for the next homework (or for the next test).

Some useful references:

S. I. Resnick, A Probability Path, Birkhauser 2001.
Richard Durrett, Probability: Theory and Examples, Wadsworth Brooks/Cole, 1991.
David Williams, Probability with Martingales, Cambridge University Press, 1991.

Click here for Prof. Sawyer's home page:

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    Last modified December 11, 2003