STA 2211S: Graduate Probability II (Spring, 2003)

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

Time and place: Wednesdays, 11:10-2:00, Sidney Smith Hall room 1074. [First class January 8; no class February 19 (Reading Week).]

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 (first one to be held on reserve in math/stat library, last two at Gerstein):

• 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: Homework assignments 40%; in-class quizzes 40%; attendance and class participation 20%.

Tentative Schedule: Quizzes: four, each 20 min long, at beginning of class on Jan 29, Feb 26, Mar 19, and Apr 9. Homework: three, each assigned in class, then due on a Friday at 3:00 pm; (#1) assigned Jan 22, due Feb 7; (#2) assigned Feb 26, due Mar 14; (#3) assigned Mar 26, due Apr 11.

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