A condition for the equivalence of coupling and shift coupling

Authors
Cranston, M Wang, FY
Citation
M. Cranston et Fy. Wang, A condition for the equivalence of coupling and shift coupling, ANN PROBAB, 28(4), 2000, pp. 1666-1679
Citations number
23
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
28
Issue
4
Year of publication
2000
Pages
1666 - 1679
Database
ISI
SICI code
0091-1798(200010)28:4<1666:ACFTEO>2.0.ZU;2-#
Abstract
It is proved in this paper that a weak parabolic Harnack inequality for a M arkov semigroup implies the existence of a coupling and a shift coupling fo r the corresponding process with equal chances of success. This implies equ ality 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 bound ed harmonic functions.