{
  "id": "2311.12294",
  "version": "v1",
  "published": "2023-11-21T02:32:27.000Z",
  "updated": "2023-11-21T02:32:27.000Z",
  "title": "On a class of stochastic fractional heat equations",
  "authors": [
    "Jian Song",
    "Meng Wang",
    "Wangjun Yuan"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Considering the stochastic fractional heat equation driven by Gaussian noise with the covariance function defined by the heat kernel, we establish Feynman-Kac formulae for both Stratonovich and Skorohod solutions, along with their respective moments. One motivation lies in the occurrence of this equation in the study of a random walk in random environment which is generated by a field of independent random walks starting from a Poisson field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-21T02:32:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60",
      "60G60"
    ],
    "keywords": [
      "stochastic fractional heat equation driven",
      "independent random walks",
      "poisson field",
      "covariance function",
      "heat kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}