{
  "id": "1103.5228",
  "version": "v3",
  "published": "2011-03-27T15:54:10.000Z",
  "updated": "2012-09-24T14:23:38.000Z",
  "title": "Weak invariance principle for the local times of partial sums of Markov Chains",
  "authors": [
    "Michael Bromberg",
    "Zemer Kosloff"
  ],
  "comment": "This is the pre galley proof version of the article; Journal of Theoretical Probability 2012",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let X_{n} be an integer valued Markov Chain with finite state space. Let S_{n}=\\sum_{k=0}^{n}X_{k} and let L_{n}(x) be the number of times S_{k} hits x up to step n. Define the normalized local time process t_{n}(x) by t_{n}(x)=\\frac{L_{n}(\\sqrt{n}(x)}{\\sqrt{n}}. The subject of this paper is to prove a functional, weak invariance principle for the normalized sequence t_{n}, i.e. we prove that under some assumptions about the Markov Chain, the normalized local times converge in distribution to the local time of the Brownian Motion.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-09-24T14:23:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "60J10"
    ],
    "keywords": [
      "weak invariance principle",
      "partial sums",
      "finite state space",
      "integer valued markov chain",
      "normalized local time process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.5228B"
    }
  }
}