STA 2211S: Graduate Probability II (Spring, 2005)

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: Mondays 1-4. First class Jan 3. Last class April 4. No classes Jan 10, Feb 14.

Place: Sidney Smith Hall, room 1072.

Textbook: Rosenthal, J.S. (2000), A First Look at Rigorous Probability Theory. Singapore: World Scientific Publishing. Available at U of T Bookstore or from www.wspc.com.

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%).

Schedule: Test #1 February 21, Test #2 April 4, each one hour long at beginning of class. Homework #1 assigned Jan 17, due by Feb 3 2:30 p.m.; Homework #2 assigned Feb 21, due by March 10 2:30 p.m.; Homework #3 assigned March 21, due by April 7 2:30 p.m.

Note: To avoid conflict of interest, the instructor will refund $2 (his approximate royalties) to each student who purchases the textbook.