Abstract
A pair (X, Y) of Markov processes on a metric space 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 inf t ≥ 0 dist(X t , Y t ) > 0 with positive probability. We investigate whether shy couplings exist for several classes of Markov processes.
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Research partially supported by NSF grant DMS-0303310 (KB and ZC).
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Benjamini, I., Burdzy, K. & Chen, ZQ. Shy couplings. Probab. Theory Relat. Fields 137, 345–377 (2007). https://doi.org/10.1007/s00440-006-0008-3
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DOI: https://doi.org/10.1007/s00440-006-0008-3