STA 2111F: Graduate Probability I (Fall, 1997)

STA 2111F is a course designed for Master's and Ph.D. level students in statistics, mathematics, and other departments, who are interested in a rigorous, mathematical treatment of probability theory using measure theory.

Instructor: Professor Jeffrey Rosenthal (contact me, Sid Smith room 6024, phone (416) 978-4594)

Time: Tuesdays, 1:00 to 4:00 pm, Mechanical Engineering room 254.

Textbook: "Probability and Measure", 3rd ed., by Patrick Billingsley. (John Wiley & Sons, 1995. Available at U of T Bookstore, $90.95.)

Content: We will largely follow the textbook, though the order of certain topics will be changed. A rough outline is that Chapters 1 and 4 will be covered, with necessary measure-theoretic material from Chapters 2 and 3 introduced as needed. Specific topics to be covered include: probability measures, the extension theorem, random variables, distributions, expectations, laws of large numbers, Markov chains. (The follow-up course, STA 2211S, will then cover chapters 5, 6, and 7, including weak convergence, characteristic functions, central limit theorems, Radon-Nykodym Theorem and Lebesgue Decomposition, conditional probability and expectation, martingales, and Kolmogorov's Existence Theorem.)

Prerequisites: Students should have a strong undergraduate background in Real Analysis, including calculus, sequences and series, elementary set theory, and epsilon-delta proofs, at the level of (say) "Elementary Classical Analysis", by Jerrold E. Marsden (W.F. Freeman and Co., 1974).

Evaluation: Homework assignments 65%; attendance and class participation 35%.

Course homework assignments -- tentative.