  This note extends the work of Foss and Tweedie (1997), who showed that
availability of the classic Coupling from The Past algorithm of Propp and
Wilson (1996) is essentially equivalent to uniform ergodicity for a Markov
chain (see also HobertRobert, 2004). In this note we show that all
geometrically ergodic chains possess dominated Coupling from The Past
algorithms (not necessarily practical!) which are rather closely connected to
Foster-Lyapunov criteria.
