{
  "id": "1711.07532",
  "version": "v1",
  "published": "2017-11-20T20:33:07.000Z",
  "updated": "2017-11-20T20:33:07.000Z",
  "title": "Path properties of the solution to the stochastic heat equation with Lévy noise",
  "authors": [
    "Carsten Chong",
    "Robert C. Dalang",
    "Thomas Humeau"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider sample path properties of the solution to the stochastic heat equation, in $\\mathbb{R}^d$ or bounded domains of $\\mathbb{R}^d$, driven by a L\\'evy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solution is shown to have a c\\`adl\\`ag modification in fractional Sobolev spaces of index less than $-\\frac d 2$. Concerning the partial regularity of the solution in time or space when the other variable is fixed, we determine critical values for the Blumenthal-Getoor index of the L\\'evy noise such that noises with a smaller index entail continuous sample paths, while L\\'evy noises with a larger index entail sample paths that are unbounded on any non-empty open subset. Our results apply to additive as well as multiplicative L\\'evy noises, and to light- as well as heavy-tailed jumps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-20T20:33:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60G17",
      "60G51",
      "60G52"
    ],
    "keywords": [
      "stochastic heat equation",
      "path properties",
      "lévy noise",
      "entail continuous sample paths",
      "index entail continuous sample"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}