{
  "id": "1801.09164",
  "version": "v1",
  "published": "2018-01-28T01:38:01.000Z",
  "updated": "2018-01-28T01:38:01.000Z",
  "title": "Another look into the Wong-Zakai Theorem for Stochastic Heat Equation",
  "authors": [
    "Yu Gu",
    "Li-Cheng Tsai"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Consider the heat equation driven by a smooth, Gaussian random potential: \\begin{align*} \\partial_t u_{\\varepsilon}=\\tfrac12\\Delta u_{\\varepsilon}+u_{\\varepsilon}(\\xi_{\\varepsilon}-c_{\\varepsilon}), \\ \\ t>0, x\\in\\mathbb{R}, \\end{align*} where $\\xi_{\\varepsilon}$ converges to a spacetime white noise, and $c_{\\varepsilon} $ is a diverging constant chosen properly. For any $ n\\geq 1 $, we prove that $ u_{\\varepsilon} $ converges in $ L^n $ to the solution of the stochastic heat equation. Our proof is probabilistic, hence provides another perspective of the general result of Hairer and Pardoux \\cite{Hairer15a}, for the special case of the stochastic heat equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-28T01:38:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic heat equation",
      "wong-zakai theorem",
      "gaussian random potential",
      "heat equation driven",
      "spacetime white noise"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}