MATH Probability II Course book Probability Theory and Examples
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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.