Gaussian Random Variables (The Normal and the Multivariate Normal Distributions), Convergence of Random Variables, Weak Convergence, Weak Convergence and Characteristic Functions, The Laws of Large Numbers, The Central Limit Theorem, L2 and Hilbert Spaces, Conditional Expectation, Martingales, Supermartingales and Submartingales, Martingale Inequalities, Martingale Convergence Theorems, The Radon-Nikodym Theorem. (3 credit hours).
