{
  "id": "1609.00769",
  "version": "v1",
  "published": "2016-09-02T23:56:09.000Z",
  "updated": "2016-09-02T23:56:09.000Z",
  "title": "A probabilistic Harnack inequality and strict positivity of stochastic partial differential equations",
  "authors": [
    "Zhenan Wang"
  ],
  "comment": "27 pages and 7 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "Under general conditions we show an a priori probabilistic Harnack inequality for the non-negative solution of a stochastic partial differential equation of the following form d_tu = div (A\\nabla u) + f (t, x, u;w) + g_i(t, x, u;w)\\dot{w}^i_t. We will also show that the solution of the above equation will be almost surely strictly positive if the initial condition is non-negative and not identically vanishing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-02T23:56:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic partial differential equation",
      "strict positivity",
      "priori probabilistic harnack inequality",
      "initial condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}