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In the past 5 years, a series of verification algorithms has been proposed for infinite Markov chains that have a finite attractor, i.e., a set that will be visited infinitely often almost surely starting from any state. In this paper, we establish a sufficient criterion for the existence of an attractor. We show that if the states of a Markov chain can be given levels (positive integers) such that the expected next level for states at some level n>0 is less than n-Δ for some positive Δ, then the states at level 0 constitute an attractor for the chain. As an application, we obtain a direct proof that some probabilistic channel systems combining message losses with duplication and insertion errors have a finite attractor.
Nathalie Bertrand
nathalie.bertrand@irisa.fr
@article{BBS-ipl06,
Author = {Baier, C. and Bertrand, N. and Schnoebelen, Ph.},
Title = {A note on the attractor-property of infinite-state {M}arkov chains},
Journal = {Information Processing Letters},
Volume = {97},
Number = {2},
Pages = {58--63},
Publisher = {Elsevier Science Publishers},
Month = {January},
Year = {2006}
}
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