Bressaud X., Fernandez R., Galves A.
Speed of $\overline d$-convergence for Markov approximations of chains
with complete connections.  A coupling approach 
(62K, LaTeX)

ABSTRACT.  We compute the speed of convergence of the canonical Markov
approximation of a chain with complete connections with summable
decays.  We show that in the $\overline{d}$-topology the approximation
converges at least at a rate proportional to these decays.
This is proven by explicitly constructing a coupling between
the chain and each range-$k$ approximation.