March 3, 2026Open Access

Shy Couplings

Key Points

Shy couplings for Markov processes demonstrate that dist(X_t, Y_t) > epsilon for all t >= 0.
Findings suggest certain conditions lead to the existence of shy couplings in Markov processes.
Exploration includes different classes of Markov processes to understand coupling behavior and properties.
Existence of shy couplings may highlight fundamental aspects of Markov processes and their transitions.

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.

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Cite this study

Benjamini et al. (Sat,) studied this question.

www.synapsesocial.com/papers/69a75fd7c6e9836116a2bfb3

Authors

Itaï Benjamini

Krzysztof Burdzy

Zhen-Qing Chen

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Shy Couplings

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion