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.
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Benjamini et al. (Sat,) studied this question.
Itaï Benjamini
Krzysztof Burdzy
Zhen-Qing Chen
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