Introduction to Probability using Measure Theory
This course will be an introduction to the issues and techniques of probability theory, at the graduate level. The topics covered will include: (i) The measure theoretic framework of modern probability theory; probability spaces and random variables; (ii) Independence and zero-one laws; (iii) Laws of large numbers and Kolmogorov's three series theorem; (iv) Convergence in distribution and the Central Limit Theorem; (v) Conditional Expectation; (vi) An introduction to martingales in discrete-time and applications to Markov chains. Time permitting, we will try to give brief introduction to large deviations and Brownian motion.
Probability with martingales by David Williams
Real Analysis (640:501 or an equivalent) is an essential prerequisite. Students should also have had an undergraduate course, at the level of Ross's text, A First Course in Probability, so that they have a basic familiarity with elementary, combinatorial probability and with the binomial, Poisson, exponential, and normal distributions.
Sections Taught this Semester:
For more information on instructors and sections for Spring 2018, please see our Spring 2018 Teaching Schedule Page
For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page