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arXiv · 0704.0508

Invariance principle for additive functionals of Markov chains

Yuri N. Kartashov·Alexey M. Kulik
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Abstract

We consider a sequence of additive functionals {ϕ_n}, set on a sequence of Markov chains {X_n} 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 probabilities of the chains X_n is proved.

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Yuri N. Kartashov, Alexey M. Kulik. 2007-04-04. Invariance principle for additive functionals of Markov chains. https://arxiv.org/abs/0704.0508

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