STA 2211S: Graduate Probability II (Spring, 2006)

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto
Sidney Smith Hall, room 6024; phone (416) 978-4594; http://probability.ca/jeff/;

Time: Tuesdays 2-5. First class Jan 10. Last class April 11. No class Feb 21 (Reading Week).

Place: Sidney Smith Hall, room 1069.

Textbook: Rosenthal, J.S. (2000), A First Look at Rigorous Probability Theory. Singapore: World Scientific Publishing. Available at the U of T Bookstore or from www.wspc.com. See also the book's errata, in compressed postscript or PDF.

Further Reading (available on short-term loan in the math/stat library):

• P. Billingsley (1995), Probability and measure (3rd ed.). John Wiley & Sons, New York.
• R. Durrett (1996), Probability: theory and examples (2nd ed.). Duxbury Press, New York.
• B. Fristedt and L. Gray (1997), A modern approach to probability theory. Birkhauser, Boston.

Content: We will cover approximately the second half of the textbook, including weak convergence, characteristic functions, central limit theorems, the Radon-Nykodym Theorem, Lebesgue Decomposition, conditional probability and expectation, martingales, and Kolmogorov's Existence Theorem. Additional topics will be presented as time allows.

Prerequisites: Students should have taken STA 2111F or equivalent.

Evaluation: Test #1 (20%), Test #2 (20%), homework assignments (36%), class participation (24%).

Tentative Schedule: Test #1 February 28, Test #2 April 11, each one hour long in class.
Homework #1 assigned Jan 24, due by Feb 9, 3:00 p.m.;
Homework #2 assigned Feb 28, due by March 17, 3:00 p.m.;
Homework #3 assigned March 28, due by April 13, 3:00 p.m.