{
  "id": "2305.02425",
  "version": "v1",
  "published": "2023-05-03T20:33:56.000Z",
  "updated": "2023-05-03T20:33:56.000Z",
  "title": "Stochastic wave equation with additive fractional noise: solvability and global Hölder continuity",
  "authors": [
    "Shuhui Liu",
    "Yaozhong Hu",
    "Xiong Wang"
  ],
  "comment": "27 pages, 2 figures",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We give the necessary and sufficient condition for the solvability of the stochastic wave equation $ \\frac{\\partial^2 }{\\partial t^2}u(t,x) =\\Delta u(t,x)+\\dot{W}(t,x)$ on $\\mathbb{R}^d$, where $W(t,x)$ is a fractional Brownian field with temporal Hurst parameter $H_0>1/2$ and spatial Hurst parameters $H_i\\in(0,1)$ for $i=1,\\cdots,d$. Moreover, we obtain the growth rate and the H\\\"older continuity of the solution on the whole space $\\mathbb{R}^d$ when $d=1$ and $H_0=1/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-03T20:33:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60H05",
      "60G15",
      "60G22"
    ],
    "keywords": [
      "stochastic wave equation",
      "global hölder continuity",
      "additive fractional noise",
      "solvability",
      "fractional brownian field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}