Theory of Probability II

Part two of a two semester course that provides an introduction to probability theory based on measure theory. Standard topics covered in the second-semester ( APMA 2640 ) include the following: discrete time martingale theory, weak convergence (also called convergence in distribution) and the central limit theorem, and a study of Brownian motion. Optional topics include the ergodic theorem and large deviation theory. Prerequisites—undergraduate probability and analysis, co-requisite—graduate real analysis.