Abstract
AbstractConsider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an independent and identically distributed (i.i.d.) process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of
${\mathbb {Z}}$
is a finitary factor of an i.i.d. process.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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