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 Wfunctionals. 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 eprints
 Pub Date:
 April 2007
 arXiv:
 arXiv:0704.0508
 Bibcode:
 2007arXiv0704.0508K
 Keywords:

 Mathematics  Probability;
 60J55;
 60F17
 EPrint:
 18 pages