{
  "id": "0704.0508",
  "version": "v1",
  "published": "2007-04-04T07:28:14.000Z",
  "updated": "2007-04-04T07:28:14.000Z",
  "title": "Invariance principle for additive functionals of Markov chains",
  "authors": [
    "Yuri N. Kartashov",
    "Alexey M. Kulik"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-04T07:28:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J55",
      "60F17"
    ],
    "keywords": [
      "additive functionals",
      "markov chains",
      "invariance principle",
      "general sufficient condition",
      "markov process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.0508K"
    }
  }
}