{
  "id": "2409.13880",
  "version": "v1",
  "published": "2024-09-20T20:18:59.000Z",
  "updated": "2024-09-20T20:18:59.000Z",
  "title": "Regularisation of cylindrical Lévy processes in Besov spaces",
  "authors": [
    "Matthew Griffiths",
    "Markus Riedle"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work, we quantify the irregularity of a given cylindrical L\\'evy process $L$ in $L^2({\\mathbb R}^d)$ by determining the range of weighted Besov spaces $B$ in which $L$ has a regularised version $Y$, that is a stochastic process $Y$ in the classical sense with values in $B$. Our approach is based on characterising L\\'evy measures on Besov spaces. As a by-product, we determine those Besov spaces $B$ for which the embedding of $L^2({\\mathbb R}^d)$ into $B$ is $0$-Radonifying and $p$-Radonifying for $p>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-20T20:18:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G20",
      "47B10",
      "60H25",
      "60G51",
      "60E07"
    ],
    "keywords": [
      "cylindrical lévy processes",
      "regularisation",
      "weighted besov spaces",
      "stochastic process",
      "characterising levy measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}