{
  "id": "1612.09440",
  "version": "v1",
  "published": "2016-12-30T10:07:35.000Z",
  "updated": "2016-12-30T10:07:35.000Z",
  "title": "Ito formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties",
  "authors": [
    "S. Albeverio",
    "L. Gawarecki",
    "V. Mandrekar",
    "B. Rüdiger",
    "B. Sarkar"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We use Yosida approximation to find an It\\^o formula for mild solutions $\\left\\{X^x(t), t\\geq 0\\right\\}$ of SPDEs with Gaussian and non-Gaussian coloured noise, the non Gaussian noise being defined through compensated Poisson random measure associated to a L\\'evy process. The functions to which we apply such It\\^o formula are in $C^{1,2}([0,T]\\times H)$, as in the case considered for SDEs in [9]. Using this It\\^o formula we prove exponential stability and exponential ultimate boundedness properties in mean square sense for mild solutions. We also compare such It\\^o formula to an It\\^o formula for mild solutions introduced by Ichikawa in [8], and an It\\^o formula written in terms of the semigroup of the drift operator [11] which we extend before to the non Gaussian case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-30T10:07:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G15",
      "60G51",
      "47A58",
      "34D05",
      "20Mxx"
    ],
    "keywords": [
      "mild solutions",
      "ito formula",
      "non-gaussian noise",
      "stability properties",
      "exponential ultimate boundedness properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}