Department of Mathematics and Statistics
McGill University
MATH 589 Advanced Probability Theory II

MATH 589 Advanced Probability Theory (4 credits). (Prerequisite: MATH 587 or equivalent.) Martingales and martingale convergence theorems (if not covered in 587). Weak convergence of measures. Characteristic functions: elementary properties, inversion formula, uniqueness and continuity theorems. Lindeberg-Feller Central Limit Theorem, infinitely divisible laws, stable laws. If time permits: Brownian motion and its properties.

Textbook: Billingsley, P. (1995). Probability and Measure 3rd Ed. Wiley-Interscience, New York. (Sections 25-30, 35, extra topics)

References:
Ash, R. B. and C.A. Doleans-Dade. (2000). Probability and Measure Theory, 2nd Ed. Academic Press. (Chapters 6,7,9 approximately)
Billingsley, P. (2000). Convergence of Probability Measures, 2nd Ed., Wiley, New York.
Chow, Y. S. and H. Teicher (1997). Probability Theory: Independence, Interchangeability, Martingales, 3rd Ed. Springer-Verlag, New York.
Chung, K. L. (2001). A Course in Probability Theory, 3rd Ed. Academic Press, San Diego.
Dudley, R. M. (1989). Real Analysis and Probability. Wadsworth, Pacific Grove, California.
Durrett, Richard (1996). Probability: Theory and Examples 2nd Ed. Duxbury, Belmont, California.
Feller, William (1971). An Introduction to Probability Theory and Its Applications, Volume II 2nd Ed. Wiley, New York.
Hoffmann-Jorgensen, J. (1994). Probability with a View Toward Statistics, Volumes I and II. Chapman-Hall, New York.
Resnick, S. I. (2001). A Probability Path. Birkhauser, Boston.
Stoyanov, J. (1997). Counterexamples in Probability, 2nd Ed. Wiley, New York.
Stromberg, K. (1994). Probability for Analysts. Chapman-Hall, New York.

Assignments: Assignments must be submitted by 5 p.m. on the due date, after which they will not be accepted. They may be handed in at the end of class, or deposited in the slot by the Math Office on the tenth floor of Burnside Hall. In the latter case, make sure you write the course number MATH 589 and instructor's name prominently on the front of your assignment (as well as your own name and student number, of course).

Marking Scheme:

Your final mark for the course will be the greater of the marks computed from these two formulas. Those students who do not write the midterm will be marked according to formula II. If needed, there will be a supplemental examination. No special writings of the final examination can be arranged, other than those officially prescribed by the University.

W. J. Anderson
Burnside Hall 1245
Tel: 398-3848
email:bill@math.mcgill.ca
http://www.math.mcgill.ca/anderson/589/589.html

589 Notes (pdf file)

Assignment: #1 ,#2, #3 , #4

Solutions to Assignments: #1 ,#2 , #3 ,#4