Correction : perfect simulation for a class of positive recurrent Markov chains

Abstract

In [1] we introduced a class of positive recurrent Markov chains, named tame chains. A perfect simulation algorithm, based on the method of dominated CFTP, was then shown to exist in principle for such chains. The construction of a suitable dominating process was flawed, in that it relied on an incorrectly stated lemma ([1], Lemma 6). This claimed that a geometrically ergodic chain, subsampled at a stopping time σ , satisfies a geometric Foster–Lyapunov drift condition with coefficients not depending on σ. This is true if σ is a stopping time independent of the chain, but not if this independence does not hold. Reference [1], Lemma 6 is therefore false as stated