{
  "id": "1407.4080",
  "version": "v1",
  "published": "2014-07-15T18:13:36.000Z",
  "updated": "2014-07-15T18:13:36.000Z",
  "title": "SPDEs with fractional noise in space with index $H<1/2$",
  "authors": [
    "Raluca Balan",
    "Maria Jolis",
    "Lluis Quer-Sardanyons"
  ],
  "comment": "40 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we consider the stochastic wave and heat equations on $\\mathbb{R}$ with non-vanishing initial conditions, driven by a Gaussian noise which is white in time and behaves in space like a fractional Brownian motion of index $H$, with $1/4<H<1/2$. We assume that the diffusion coefficient is given by an affine function $\\sigma(x)=ax+b$, and the initial value functions are bounded and H\\\"older continuous of order $H$. We prove the existence and uniqueness of the mild solution for both equations. We show that the solution is $L^{2}(\\Omega)$-continuous and its $p$-th moments are uniformly bounded, for any $p \\geq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-15T18:13:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H05"
    ],
    "keywords": [
      "fractional noise",
      "initial value functions",
      "fractional brownian motion",
      "stochastic wave",
      "mild solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4080B"
    }
  }
}