{
  "id": "1309.6429",
  "version": "v1",
  "published": "2013-09-25T08:48:06.000Z",
  "updated": "2013-09-25T08:48:06.000Z",
  "title": "Weak Convergence to Stable Lévy Processes for Nonuniformly Hyperbolic Dynamical Systems",
  "authors": [
    "Ian Melbourne",
    "Roland Zweimüller"
  ],
  "comment": "Accepted for publication in Ann. Inst. H. Poincar\\'e (B) Probab. Statist",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider weak invariance principles (functional limit theorems) in the domain of a stable law. A general result is obtained on lifting such limit laws from an induced dynamical system to the original system. An important class of examples covered by our result are Pomeau-Manneville intermittency maps, where convergence for the induced system is in the standard Skorohod J_1 topology. For the full system, convergence in the J_1 topology fails, but we prove convergence in the M_1 topology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-25T08:48:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "28D05",
      "37A50",
      "60F17"
    ],
    "keywords": [
      "nonuniformly hyperbolic dynamical systems",
      "stable lévy processes",
      "weak convergence",
      "weak invariance principles",
      "functional limit theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6429M"
    }
  }
}