{
  "id": "1409.5687",
  "version": "v1",
  "published": "2014-09-19T15:04:26.000Z",
  "updated": "2014-09-19T15:04:26.000Z",
  "title": "Moment bounds for a class of fractional stochastic heat equations",
  "authors": [
    "Mohammud Foondun",
    "Wei Liu",
    "McSylvester Omaba"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider fractional stochastic heat equations of the form $\\frac{\\partial u_t(x)}{\\partial t} = -(-\\Delta)^{\\alpha/2} u_t(x)+\\lambda \\sigma (u_t(x)) \\dot F(t,\\, x)$. Here $\\dot F$ denotes the noise term. Under suitable assumptions, we show that the second moment of the solution grows exponentially with time. In particular, this answers an open problem in \\cite{CoKh}. Along the way, we prove a number of other interesting properties which extend and complement results in \\cite{foonjose}, \\cite{Khoshnevisan:2013aa} and \\cite{Khoshnevisan:2013ab}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-19T15:04:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional stochastic heat equations",
      "moment bounds",
      "noise term",
      "second moment",
      "solution grows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5687F"
    }
  }
}