{
  "id": "1910.04934",
  "version": "v1",
  "published": "2019-10-11T01:43:21.000Z",
  "updated": "2019-10-11T01:43:21.000Z",
  "title": "Transportation inequalities under uniform metric for a stochastic heat equation driven by time-white and space-colored noise",
  "authors": [
    "Shijie shang",
    "Ran Wang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we prove transportation inequalities on the space of continuous paths with respect to the uniform metric, for the law of solution to a stochastic heat equation defined on $[0,T]\\times [0,1]^d$. This equation is driven by the Gaussian noise, white in time and colored in space. The proof is based on a new moment inequality under the uniform metric for the stochastic convolution with respect to the time-white and space-colored noise, which is of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-11T01:43:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "60H15"
    ],
    "keywords": [
      "stochastic heat equation driven",
      "uniform metric",
      "transportation inequalities",
      "space-colored noise",
      "time-white"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}