{
  "id": "2007.10203",
  "version": "v1",
  "published": "2020-07-20T15:37:32.000Z",
  "updated": "2020-07-20T15:37:32.000Z",
  "title": "Exact asymptotics of the stochastic wave equation with time-independent noise",
  "authors": [
    "Raluca M. Balan",
    "Le Chen",
    "Xia Chen"
  ],
  "comment": "39 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we study the stochastic wave equation in all dimensions $d\\leq 3$, driven by a Gaussian noise $\\dot{W}$ which does not depend on time. We assume that either the noise is white, or the covariance function of the noise satisfies a scaling property similar to the Riesz kernel. The solution is interpreted in the Skorohod sense using Malliavin calculus. We obtain the exact asymptotic behaviour of the $p$-th moment of the solution either when the time is large or when $p$ is large. For the critical case, that is the case when $d=3$ and the noise is white, we obtain the exact transition time for the second moment to be finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T15:37:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic wave equation",
      "time-independent noise",
      "exact asymptotic behaviour",
      "exact transition time",
      "property similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}