{
  "id": "1812.05019",
  "version": "v1",
  "published": "2018-12-12T16:43:01.000Z",
  "updated": "2018-12-12T16:43:01.000Z",
  "title": "A Central Limit Theorem for the stochastic wave equation with fractional noise",
  "authors": [
    "Francisco Delgado-Vences",
    "David Nualart",
    "Guangqu Zheng"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the one-dimensional stochastic wave equation driven by a Gaussian multiplicative noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\\in [1/2,1)$ in the spatial variable. We show that the normalized spacial average of the solution over $[-R,R]$ converges in total variation distance to a normal distribution, as $R$ tends to infinity. We also provide a functional central limit theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-12T16:43:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H07",
      "60G15",
      "60F05"
    ],
    "keywords": [
      "fractional noise",
      "one-dimensional stochastic wave equation driven",
      "functional central limit theorem",
      "total variation distance",
      "fractional brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}