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October 2000 A condition for the equivalence of coupling and shift coupling
M. Cranston, Feng-Yu Wang
Ann. Probab. 28(4): 1666-1679 (October 2000). DOI: 10.1214/aop/1019160502


It is proved in this paper that a weak parabolic Harnack inequality for a Markov semigroup implies the existence of a coupling and a shift coupling for the corresponding process with equal chances of success. This implies equality of the tail and invariant $\sigma$-fields for the diffusion as well as equality of the class of bounded parabolic functions and the class of bounded harmonic functions.


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M. Cranston. Feng-Yu Wang. "A condition for the equivalence of coupling and shift coupling." Ann. Probab. 28 (4) 1666 - 1679, October 2000.


Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60066
MathSciNet: MR1813838
Digital Object Identifier: 10.1214/aop/1019160502

Primary: 60J45. , 60J60

Keywords: coupling , invariant $\sigma$-field , parabolic inequality , shift coupling , tail $\sigma$-field

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.28 • No. 4 • October 2000
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