{
  "id": "1001.4013",
  "version": "v3",
  "published": "2010-01-22T15:04:54.000Z",
  "updated": "2012-03-07T10:30:55.000Z",
  "title": "Stochastic evolution equations driven by Liouville fractional Brownian motion",
  "authors": [
    "Zdzislaw Brzezniak",
    "Jan van Neerven",
    "Donna Salopek"
  ],
  "comment": "To appear in Czech. Math. J",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval (0,1). For Hurst parameters in (0,1/2) we show that a function F:(0,T)\\to L(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fBm if and only if it is stochastically integrable with respect to an H-cylindrical fBm with the same Hurst parameter. As an application we show that second-order parabolic SPDEs on bounded domains in \\mathbb{R}^d, driven by space-time noise which is white in space and Liouville fractional in time with Hurst parameter in (d/4,1) admit mild solution which are H\\\"older continuous both and space.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-03-07T10:30:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "35R60",
      "47D06",
      "60G18"
    ],
    "keywords": [
      "stochastic evolution equations driven",
      "hurst parameter",
      "h-cylindrical liouville fractional brownian motions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.4013B"
    }
  }
}