Invariance principle for additive functionals of Markov chains
@inproceedings{NKartashov2007InvariancePF,
title={Invariance principle for additive functionals of Markov chains},
author={Yuri N.Kartashov and Alexey M.Kulik},
year={2007}
}We consider a sequence of additive functionals {φn}, set on a sequence of Markov chains {Xn} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms of the characteristics of the additive functionals, and related to the Dynkin’s theorem on the convergence of W -functionals. As an application of the main theorem, the general sufficient condition for convergence of additive functionals in terms of transition… Expand
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