{
  "id": "0905.2150",
  "version": "v1",
  "published": "2009-05-13T17:10:36.000Z",
  "updated": "2009-05-13T17:10:36.000Z",
  "title": "$L_p$-Theory for the Stochastic Heat Equation with Infinite-Dimensional Fractional Noise",
  "authors": [
    "Raluca Balan"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we consider the stochastic heat equation $du=(\\Delta u+f(t,x))dt+ \\sum_{k=1}^{\\infty} g^{k}(t,x) \\delta \\beta_t^k, t \\in [0,T]$, with random coefficients $f$ and $g^k$, driven by a sequence $(\\beta^k)_k$ of i.i.d. fractional Brownian motions of index $H>1/2$. Using the Malliavin calculus techniques and a $p$-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to $(\\beta^k)_k$, we prove that the equation has a unique solution (in a Banach space of summability exponent $p \\geq 2$), and this solution is H\\\"older continuous in both time and space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-13T17:10:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H07"
    ],
    "keywords": [
      "stochastic heat equation",
      "infinite-dimensional fractional noise",
      "th moment maximal inequality",
      "malliavin calculus techniques",
      "fractional brownian motions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.2150B"
    }
  }
}