STAT 6542: Advanced Probability Theory
(Cross-listed with MATH 6542).
Credits: 3. Contact Hours: Lecture 3.
Prereq: STAT 6541 or (MATH 5150 and STAT 5543)
Probability spaces and random variables. Kolmogorov's consistency theorem. Independence, Borel-Cantelli lemmas and Kolmogorov's 0 - 1 Law. Types and characterizations of convergence for random variables. Sums of independent random variables, empirical distributions, weak and strong laws of large numbers. Convergence in distribution and its formulations, tightness, characteristic functions, central limit theorems and Lindeberg-Feller conditions. Conditional probability and expectation, discrete parameter martingales.
(Typically Offered: Spring)