Theory of Probability II

3 credits · Graduate Programs

Stopping times, renewal theory, martingales, almost sure convergence, Radon-Nikodym derivatives, Doob's inequality, square integrable martingales, uniform integrability, Markov chains, stationary measure, Birkhoff's Ergodic Theorem, Brownian motion, stopping times, hitting times, Donsker's Theorem, Brownian bridge, laws of the iterated logarithm. Prerequisite(s): Statistics 701 and admission to a graduate program in Mathematics and Statistics or consent of the Department.