This is a graduate level course on probability. The course starts with a quick review of measure-based probability. Even though an earlier exposition to measure theory would be helpful, it is not crucial as we will build the necessary background. The course will then discuss a variety of limit theorems for independent and dependent variables that appear in many areas of statistics, stochastic analysis, and econometrics. The second part of the course will discuss some more advanced topics of stochastic processes. Topics include conditional probability and expectation, martingale thoery, Brownian motion and other related Gaussian Processes, and the Invariance Principle. Depending on time, additional topics such as Poisson and L\'evy processes and more general semimartingales, may be covered.
Section 01TOPICS IN ADVANCED PROBABILITY
INSTRUCTOR: Figueroa-LopezView Course Listing