Theory of Probability

4.0 credits

Measure-theoretic foundations of probability. The Radon-Nikodym theorem and conditional expectation. Infinite products and Kolmogorov's extension theorem. Random variables, modes of convergence, independence, and the monotone class theorem. Laws of large numbers. Characteristic functions and the central limit theorem. Martingales, Doob's and Kolmogorov's inequalities, the optional sampling theorem. Introduction to stochastic processes.