{
  "id": "1610.06711",
  "version": "v1",
  "published": "2016-10-21T09:19:34.000Z",
  "updated": "2016-10-21T09:19:34.000Z",
  "title": "Scaling Limits of Solutions of SPDE Driven by Lévy White Noises",
  "authors": [
    "Julien Fageot",
    "Michael Unser"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a random process s solution of the stochastic partial differential equation Ls = w with L a homogeneous operator and w a multidimensional L\\'evy white noise. In this paper, we study the asymptotic effect of a zoom or a de-zoom on the process s. More precisely, we give sufficient conditions on L and w so that the rescaled versions of s converges in law to a self-similar process of order H at coarse scales and at fine scales. The parameter H depends on the homogeneity order of the operator L and the Blumenthal-Getoor indices associated to the L\\'evy white noise w. Finally, we apply our general results to several notorious classes of random processes and random fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-21T09:19:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60F05",
      "60G18",
      "60G20"
    ],
    "keywords": [
      "lévy white noises",
      "spde driven",
      "scaling limits",
      "stochastic partial differential equation ls",
      "random process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}