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Course Descriptions

16:642:591 - Topics in Probability & Ergodic Theory II

Kasper Larsen

Subtitle:

 Introduction to Probability using Measure Theory

Course Description:

 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.

Text:

 Probability with martingales by David Williams

Prerequisites:

 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.

Schedule of Sections:

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530