University of Connecticut

Course Info

MATH 5160: Probability Theory and Stochastic Processes I

Description: Foundation of probability theory, monotone classes and pi-lambda theorem, Kolmogorov extension theorem and infinite product spaces, Kolmogorov zero-one law, a.s. convergence, convergence in probability and in Lp of random variables, Borell-Cantelli lemma. Convergence of series of independent random variables: the theorems of Kolmogorov and Levy. Weak convergence of probability measures: characteristic functions, Levy-Cramer continuity theorem, tightness and Prohorov's theorem. The Central Limit Theorem: the Lindeberg-Feller theorem, the Levy-Khintchine formula, stable laws. Conditional expectation. Discrete time (sub- and super) martingales: Doob's maximal inequality, Optional Stopping Theorem, uniform integrability, and the a.s. convergence theorem for L1 bounded martingales, convergence in Lp. Definition, existence and basic properties of the Brownian Motion. Other topics in probability theory at the choice of the instructor (e.g. Markov chains, Birkhoff-Khinchine and Kigman ergodic theorems, Levy's arcsine law, Law of Iterated Logarithm, convergence to stable laws).

Prerequisites: None

Credits: 3

Sections: Fall 2011 on Storrs Campus

PSCourseID Course Sec Comp Time Room Instructor
08013 5160 001 Lecture TuTh 2:00:00 PM-3:15:00 PM MSB315 Evarist Gine-Masdeu