{
  "id": "0906.3076",
  "version": "v2",
  "published": "2009-06-17T05:53:33.000Z",
  "updated": "2010-12-09T09:07:17.000Z",
  "title": "Feynman-Kac formula for heat equation driven by fractional white noise",
  "authors": [
    "Yaozhong Hu",
    "David Nualart",
    "Jian Song"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOP547 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2011, Vol. 39, No. 1, 291-326",
  "doi": "10.1214/10-AOP547",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman-Kac formula is a weak solution of the stochastic heat equation. From the Feynman-Kac formula, we establish the smoothness of the density of the solution and the H\\\"{o}lder regularity in the space and time variables. We also derive a Feynman-Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansion of the solution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-09T09:07:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "feynman-kac formula",
      "heat equation driven",
      "fractional white noise",
      "multidimensional stochastic heat equation",
      "wiener chaos expansion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.3076H"
    }
  }
}