{
  "id": "1509.03529",
  "version": "v1",
  "published": "2015-09-11T14:22:12.000Z",
  "updated": "2015-09-11T14:22:12.000Z",
  "title": "On a limit behavior of a sequence of Markov processes perturbed in a neighborhood of a singular point",
  "authors": [
    "Andrey Pilipenko",
    "Yuriy Prykhodko"
  ],
  "comment": "17 pages",
  "journal": "Ukrainian Mathematical Journal (2015), vol.67, No.4",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a \"singular\" point attract to some probability law. In any neighborhood of this point the behavior may be irregular. As an example of the general result we consider a symmetric random walk with the unit jump that is perturbed in a neighborhood of 0. The invariance principle is obtained under standard scaling of time and space. The limit process turns out to be a skew Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-11T14:22:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17"
    ],
    "keywords": [
      "markov processes",
      "limit behavior",
      "singular point",
      "neighborhood",
      "symmetric random walk"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150903529P"
    }
  }
}