Weak convergence in Probability Theory - A summer excursion! June 17 to 21, 2013

Title: Weak convergence in Probability Theory - A summer excursion!
Author: Armand Makowski, University of Maryland, USA

Date: June 17, 2013 - June 21, 2013
Time: 9:00 - 11:00
Place: BCAM Seminar room

Abstract: In this series of five lectures we discuss various topics related to the weak convergence of random variables, also known as convergence in law or distributional convergence. We have two main (and somewhat unrelated) objectives: (i) Show how various notions of coupling can be used to establish weak convergence; (ii) Discuss how the finite-dimensional theory extends to function spaces. The lectures are tentatively organized as follows:

Day 1: Basic definitions of convergence for random variables will be reviewed, together with criteria and counter-examples.

Day 2: Skorokhod's Theorem and coupling -- Examples in queueing theory, in the theory of Markov chains and time series analysis.

Day 3: Poisson convergence: The Stein-Chen method with applications to problems in the the theory of random graphs.

Day 4: Weak convergence in function spaces -- Prohorov's Theorem and sequential compactness

Day 5: An illustration: From random walks to Brownian motion

The course will be self-contained. A basic knowledge of measure-theoretic probability theory would be helpful

• MAKOWSKI 2013 06 17 Lect Day 1
• MAKOWSKI 2013 06 18 Lect Day 2
• MAKOWSKI 2013 06 19 Lect Day 3
• BCAMCourse2013-06-17-21AM
• 17:06:13_C_Armand_Makowski.zip