{
  "id": "1404.2411",
  "version": "v3",
  "published": "2014-04-09T09:47:40.000Z",
  "updated": "2016-03-23T13:40:06.000Z",
  "title": "Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: The non-stationary case",
  "authors": [
    "Francisco J. Delgado-Vences",
    "Marta Sanz-Solé"
  ],
  "comment": "Published at http://dx.doi.org/10.3150/15-BEJ704 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2016, Vol. 22, No. 3, 1572-1597",
  "doi": "10.3150/15-BEJ704",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is a continuation of (Bernoulli 20 (2014) 2169-2216) where we prove a characterization of the support in H\\\"older norm of the law of the solution to a stochastic wave equation with three-dimensional space variable and null initial conditions. Here, we allow for non-null initial conditions and, therefore, the solution does not possess a stationary property in space. As in (Bernoulli 20 (2014) 2169-2216), the support theorem is a consequence of an approximation result, in the convergence of probability, of a sequence of evolution equations driven by a family of regularizations of the driving noise. However, the method of the proof differs from (Bernoulli 20 (2014) 2169-2216) since arguments based on the stationarity property of the solution cannot be used.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-10T06:35:24.000Z",
      "title": "Approximation of a stochastic wave equation in dimension three, with application to a support theorem in Hölder norm: the non-stationary case",
      "abstract": "This paper is a continuation of [7] where we prove a characterization of the support in H\\\"older norm of the law of the solution to a stochastic wave equation with three-dimensional space variable and null initial conditions. Here we allow for non null initial conditions and therefore the solution does not possess a stationary property in space. As in [7], the support theorem is a consequence of an approximation result, in the convergence of probability, of a sequence of evolution equations driven by a family of regularizations of the driving noise. However, the method of the proof differs from [7] since arguments based on the stationarity property of the solution cannot be used.",
      "comment": "24 pages",
      "journal": null,
      "doi": null,
      "authors": [
        "Francisco Delgado-Vences",
        "Marta Sanz-Solé"
      ]
    },
    {
      "version": "v3",
      "updated": "2016-03-23T13:40:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G60",
      "60G17",
      "35L05"
    ],
    "keywords": [
      "stochastic wave equation",
      "support theorem",
      "non-stationary case",
      "hölder norm",
      "approximation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2411D"
    }
  }
}