Shy Couplings

Abstract

A pair (X; Y) of Markov processes is called a Markov coupling if X and Y have the same transition probabilities and (X;Y) is a Markov process. We say that a coupling is "shy" if there exists a (random) [Epsilon] > 0 such that dist(X [subscript] t; Y [subscript] t) > [Epsilon] for all t [is greater than or equal to] 0. We investigate whether shy couplings exist for several classes of Markov processes.