{
  "id": "1911.12264",
  "version": "v1",
  "published": "2019-11-27T16:28:45.000Z",
  "updated": "2019-11-27T16:28:45.000Z",
  "title": "SPDEs with linear multiplicative fractional noise: continuity in law with respect to the Hurst index",
  "authors": [
    "Luca M. Giordano",
    "Maria Jolis",
    "Lluís Quer-Sardanyons"
  ],
  "comment": "33 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we consider the one-dimensional stochastic wave and heat equations driven by a linear multiplicative Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $H\\in (\\frac 14,1)$. We prove that the solution of each of the above equations is continuous in terms of the index $H$, with respect to the convergence in law in the space of continuous functions. The proof is based on a tightness criterion on the plane and Malliavin calculus techniques in order to identify the limit law.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-27T16:28:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B10",
      "60H07",
      "60H15"
    ],
    "keywords": [
      "linear multiplicative fractional noise",
      "hurst index",
      "continuity",
      "malliavin calculus techniques",
      "one-dimensional stochastic wave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}