{
  "id": "2109.09359",
  "version": "v1",
  "published": "2021-09-20T08:24:07.000Z",
  "updated": "2021-09-20T08:24:07.000Z",
  "title": "On $q$-scale functions of spectrally negative Lévy processes",
  "authors": [
    "Anita Behme",
    "David Oechsler",
    "René L. Schilling"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain series expansions of the $q$-scale functions of arbitrary spectrally negative L\\'evy processes, including processes with infinite jump activity, and use these to derive various new examples of explicit $q$-scale functions. Moreover, we study smoothness properties of the $q$-scale functions of spectrally negative L\\'evy processes with infinite jump activity. This complements previous results of Chan et al. [7] for spectrally negative L\\'evy processes with Gaussian component or bounded variation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-20T08:24:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60J45",
      "91G05"
    ],
    "keywords": [
      "spectrally negative lévy processes",
      "scale functions",
      "infinite jump activity",
      "arbitrary spectrally negative levy processes",
      "study smoothness properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}