{
  "id": "1502.05514",
  "version": "v1",
  "published": "2015-02-19T09:54:54.000Z",
  "updated": "2015-02-19T09:54:54.000Z",
  "title": "Fractional diffusion in Gaussian noisy environment",
  "authors": [
    "Guannan Hu",
    "Yaozhong Hu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic partial equations of the following form: $D_t^\\alpha u(t, x)=\\textit{B}u+u\\cdot W^H$, where $D_t^\\alpha$ is the fractional derivative of order $\\alpha$ with respect to the time variable $t$, $\\textit{B}$ is a second order elliptic operator with respect to the space variable $x\\in\\mathbb{R}^d$, and $W^H$ a fractional Gaussian noise of Hurst parameter $H=(H_1, \\cdots, H_d)$. We obtain conditions satisfied by $\\alpha$ and $H$ so that the square integrable solution $u$ exists uniquely .",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-19T09:54:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "60H15",
      "60H05",
      "35K40",
      "35R60"
    ],
    "keywords": [
      "gaussian noisy environment",
      "fractional diffusion",
      "fractional order stochastic partial equations",
      "second order elliptic operator",
      "fractional gaussian noise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}