{
  "id": "1510.04674",
  "version": "v1",
  "published": "2015-10-15T19:28:14.000Z",
  "updated": "2015-10-15T19:28:14.000Z",
  "title": "A Boundedness Trichotomy for the Stochastic Heat Equation",
  "authors": [
    "Le Chen",
    "Davar Khoshnevisan",
    "Kunwoo Kim"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the stochastic heat equation with a multiplicative white noise forcing term under standard \"intermitency conditions.\" The main finding of this paper is that, under mild regularity hypotheses, the a.s.-boundedness of the solution $x\\mapsto u(t\\,,x)$ can be characterized generically by the decay rate, at $\\pm\\infty$, of the initial function $u_0$. More specifically, we prove that there are 3 generic boundedness regimes, depending on the numerical value of $\\Lambda:= \\lim_{|x|\\to\\infty} |\\log u_0(x)|/(\\log|x|)^{2/3}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-15T19:28:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60"
    ],
    "keywords": [
      "stochastic heat equation",
      "boundedness trichotomy",
      "multiplicative white noise forcing term",
      "mild regularity hypotheses",
      "generic boundedness regimes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151004674C"
    }
  }
}