{
  "id": "1509.05274",
  "version": "v1",
  "published": "2015-09-17T14:51:23.000Z",
  "updated": "2015-09-17T14:51:23.000Z",
  "title": "Lévy Processes and Lévy White Noise as Tempered Distributions",
  "authors": [
    "Robert C. Dalang",
    "Thomas Humeau"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We identify a necessary and sufficient condition for a L\\'evy white noise to be a tempered distribution. More precisely, we show that if the L\\'evy measure associated with this noise has a positive absolute moment, then the L\\'evy white noise almost surely takes values in the space of tempered distributions. If the L\\'evy measure does not have a positive absolute moment of any order, then the event on which the L\\'evy white noise is a tempered distribution has probability zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-17T14:51:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G60",
      "60G20",
      "60H40"
    ],
    "keywords": [
      "tempered distribution",
      "lévy white noise",
      "levy white noise",
      "lévy processes",
      "positive absolute moment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150905274D"
    }
  }
}