Connor, Stephen B. and Kendall, Wilfrid S. (2007) Correction : perfect simulation for a class of positive recurrent Markov chains. Annals of Applied Probability, Vol.17 (No.5-6). pp. 1808-1810. ISSN 1050-5164

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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.

Item Type:	Journal Item
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Ergodic theory, Markov processes
Journal or Publication Title:	Annals of Applied Probability
Publisher:	Institute of Mathematical Statistics
ISSN:	1050-5164
Date:	October 2007
Volume:	Vol.17
Number:	No.5-6
Number of Pages:	3
Page Range:	pp. 1808-1810
Identification Number:	10.1214/07-AAP458
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
References:	[1] CONNOR, S. B. and KENDALL, W. S. (2007). Perfect simulation for a class of positive recurrent Markov chains. Ann. Appl. Probab. 17 781–808. [2] KENDALL, W. S. (2004). Geometric ergodicity and perfect simulation. Electron. Comm. Probab. 9 140–151. MR2108860
URI:	http://wrap.warwick.ac.uk/id/eprint/31297

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