Summary
The result linking shift-coupling to time-average total variation convergence and to the invariant σ-field is extended to continuous time and an analogous result established linking ε-couplings to smooth total variation convergence and to a smooth tail σ-field. Shift- and ε-coupling inequalities are presented.
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Thorisson, H. Shift-coupling in continuous time. Probab. Th. Rel. Fields 99, 477–483 (1994). https://doi.org/10.1007/BF01206228
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DOI: https://doi.org/10.1007/BF01206228