{
  "id": "2111.14242",
  "version": "v2",
  "published": "2021-11-28T21:32:25.000Z",
  "updated": "2023-01-31T21:54:26.000Z",
  "title": "Stochastic wave equation with Lévy white noise",
  "authors": [
    "Raluca M. Balan"
  ],
  "comment": "36 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we study the stochastic wave equation on the entire space $\\mathbb{R}^d$, driven by a space-time L\\'evy white noise with possibly infinite variance (such as the $\\alpha$-stable L\\'evy noise). In this equation, the noise is multiplied by a Lipschitz function $\\sigma(u)$ of the solution. We assume that the spatial dimension is $d=1$ or $d=2$. Under general conditions on the L\\'evy measure of the noise, we prove the existence of the solution, and we show that, as a function-valued process, the solution has a c\\`adl\\`ag modification in the local fractional Sobolev space of order $r<1/4$ if $d=1$, respectively $r<-1$ if $d=2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-01-31T21:54:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic wave equation",
      "lévy white noise",
      "space-time levy white noise",
      "local fractional sobolev space",
      "infinite variance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}