MATH Probability II Course book Probability Theory and Examples

							                             MATH 545 – Probability II

Course book Probability: Theory and Examples, 3rd edition. R. Durrett. Duxbury
Press.
Class times MWF 10.00 in MATH 202.
Office: MATH ANNEX 1209
Office hours: by appointment.
Web page: www.math.ubc.ca/∼barlow
Outline.
This course will cover parts of chapters 4, 5, 7 of Durrett’s book:
 4. Martingales, stopping times, convergence and applications.
 5. Random walks and Markov chains. Transience, recurrence, asymptotic behaviour,
    stationary measures. Examples, including branching processes.
 7. Brownian motion. Definition, construction, processes in continuous time. Basic prop-
    erties of Brownian motion.
Grading.     No midterm; course mark will be based on homeworks (50 %) and final (50
%).

Booklist for 545
(a) There are many books which cover roughly this material, i.e. a 1-year graduate prob-
ability course. Some of these are:

L. Breiman. Probability. SIAM.
P. Billingsley. Probability and Measure.
K.L. Chung. A course in probability theory.
O. Kallenberg. Foundations of Modern Probability.
D.W. Stroock. Probability Theory. An analytic view.
(b) Some other books and further reading:
D. Williams. Probability with Martingales. [Covers martingale part of the course in a
rather different way.]
I. Karatzas and S.E. Shreve: Brownian motion and stochastic calculus.