Invariance principle for additive functionals of Markov chains
Abstract
We consider a sequence of additive functionals {\phi_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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2007
- DOI:
- 10.48550/arXiv.0704.0508
- arXiv:
- arXiv:0704.0508
- Bibcode:
- 2007arXiv0704.0508K
- Keywords:
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- Mathematics - Probability;
- 60J55;
- 60F17
- E-Print:
- 18 pages