Weak convergence of additive functionals of a sequence of Markov chains

Yuri. I. Kartashov, Alexey. M. Kulik

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev 01601, Tereshchenkivska Str. 3

Abstract: We consider additive functionals $\phi_n$, $n\geq1$ defined on a sequence of Markov chains that weakly converges to a Markov process. We give sufficient condition for $\phi_n$, $n\geq1$ to converge in distribution, formulated in the terms of their characteristics (i.e. expectations). This condition generalizes Dynkin's theorem on convergence of $W$-functionals of a time homogeneous Markov process.

Keywords: Additive functional, characteristic of additive functional, $W$-functional, local time, Markov approximation.

MSC: Primary 60J55; Secondary 60F17

Language: English

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