Discrete-time stochastic analysis: Stochastic basis, filtration, stochastic sequences. Absolute continuity of probability measures and conditional expectations. Martingale-like and predictable stochastic sequences. Doob's decomposition and inequalities. Stopping times and related properties. Uniformly integrable stochastic sequences. Limit behaviour of martingales, including the Law of Large Numbers and the Central Limit Theorem. Transition from discrete-time to continuous-time stochastic analysis. Introduction to stochastic integration with respect to Brownian motion. Prerequisites: STAT 371 or STAT 281 or MATH 467 or consent of the Department.