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: 195-212
Journal Issue: 2
DOI: 10.1007/BF00354033
We consider a M a r k o v chain on (E,N) generated by a M a r k o v
kernel P. We study the question, when we can find for two initial distri-
butions v and p two r a n d o m i z e d stopping times T of (,Xn),~ N and S of
(uX,),~N, such that the distribution of ~X r equals the one of , X s and T, S
are b o t h finite.
T h e answer is given in terms of ( v - p , h ) with h b o u n d e d harmonic, or
in terms of lim
" __#) pk .
1 .3"(v
F o r stopping times T, S for two chains (~X,)n~ N, (,X,)n~ N we consider
measures t/, ~ on (E,N) defined as follows: r/(A)=expected n u m b e r of visits
of (~X,) to A before T, ~ ( A ) = e x p e c t e d n u m b e r of visits of (,X,) to A before
S.
We show that we can construct T, S such that t/ and ~ are mutually
singular and ~Lf(~Xr)=~(~Xs). We relate ~ and ~ to the positive and
negative part of certain solutions of the Poisson equation ( I - P ) ( . ) = v-/~.
APA:
Greven, A. (1987). Couplings of markov chains by randomized stopping times - Part I: Couplings, harmonic functions and the poisson equation. Probability Theory and Related Fields, 75(2), 195-212. https://dx.doi.org/10.1007/BF00354033
MLA:
Greven, Andreas. "Couplings of markov chains by randomized stopping times - Part I: Couplings, harmonic functions and the poisson equation." Probability Theory and Related Fields 75.2 (1987): 195-212.
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