{
  "id": "1406.5246",
  "version": "v1",
  "published": "2014-06-20T00:35:31.000Z",
  "updated": "2014-06-20T00:35:31.000Z",
  "title": "Analysis of the gradient of the solution to a stochastic heat equation via fractional Brownian motion",
  "authors": [
    "Mohammud Foondun",
    "Davar Khoshnevisan",
    "Pejman Mahboubi"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the stochastic partial differential equation $\\partial_t u = Lu+\\sigma(u)\\xi$, where $\\xi$ denotes space-time white noise and $L:=-(-\\Delta)^{\\alpha/2}$ denotes the fractional Laplace operator of index $\\alpha/2\\in(\\nicefrac12\\,,1]$. We study the detailed behavior of the approximate spatial gradient $u_t(x)-u_t(x-\\varepsilon)$ at fixed times $t>0$, as $\\varepsilon\\downarrow0$. We discuss a few applications of this work to the study of the sample functions of the solution to the KPZ equation as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-20T00:35:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G17",
      "60H10",
      "47B80"
    ],
    "keywords": [
      "stochastic heat equation",
      "fractional brownian motion",
      "stochastic partial differential equation",
      "denotes space-time white noise",
      "approximate spatial gradient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5246F"
    }
  }
}