A coupling of random variables or random processes is a method by which these random objects are put onto a single probability space, in such a way that their properties can be compared. Coupling is a powerful technique in probability theory and has been applied in a variety of different contexts, e.g. to prove inequalities, limit theorems, rates of convergence, and asymptotic approximations.
The course first explains what coupling is and what general
framework it fits into. After that, a number of applications
are described, taken from renewal theory, Markov chain theory, percolation, random walk, interacting particle systems, and Poisson approximation.
Voorkennis
Inleiding kansrekening
Tentaminering
Schriftelijk tentamen
Literatuur
T. Lindvall, Lectures on the Coupling Method, John Wiley & Sons, New York, 1992, ISBN 0-471-54025-0.