Greven A (1987)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1987
Publisher: Springer Verlag (Germany)
Book Volume: 75
Pages Range: 431-458
Journal Issue: 3
DOI: 10.1007/BF00318710
We consider a 0-recurrent ergodic Markov chain on (E,N),
generated by a kernel P. Again we consider couplings of two chains (~X,),
(uX,) starting with the initial distributions v respectively ~t and evolving
with P. The coupling consists of two randomized stopping times: T, S, with
~ ( ~ x T ) = ~(~,Xs).
Under additional regularity assumptions we characterize the existence of
"short" couplings for two chains (~X~), (uX~) by the property: ( v - # , h ) = 0
for all harmonic functions h fulfilling certain growth conditions. By "short"
we mean that the probability to hit CAm before T respectively S decays
faster than the analogue quantity for the recurrence times of v and #. Here
the -~m are constructed in terms of recurrence times for a certain class of
measures (.3, m T E).
We will also show that the couplings of the chains (~X~)k~, (~X~')k~
obtained by stopping the original chains, when first hitting C ~]m, converge
to a coupling of the original chains, which is also distinguished from other
exact couplings by space-time properties. We use these results to character-
ize the recurrent potential kernel.
APA:
Greven, A. (1987). Couplings of Markov chains by randomized stopping times - Part II: Short couplings for 0-recurrent chains and harmonic functions. Probability Theory and Related Fields, 75(3), 431-458. https://dx.doi.org/10.1007/BF00318710
MLA:
Greven, Andreas. "Couplings of Markov chains by randomized stopping times - Part II: Short couplings for 0-recurrent chains and harmonic functions." Probability Theory and Related Fields 75.3 (1987): 431-458.
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