{
  "id": "2309.14038",
  "version": "v1",
  "published": "2023-09-25T11:06:46.000Z",
  "updated": "2023-09-25T11:06:46.000Z",
  "title": "On the convolution equivalence of tempered stable distributions on the real line",
  "authors": [
    "Lorenzo Torricelli"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show the convolution equivalence property of univariate tempered stable distributions in the sense of Rosi\\'nsky (2007). This makes rigorous various classic heuristic arguments on the asymptotic similarity between the probability and L\\'evy densities of such distributions. Some specific examples from the literature are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-25T11:06:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E07"
    ],
    "keywords": [
      "real line",
      "classic heuristic arguments",
      "convolution equivalence property",
      "univariate tempered stable distributions",
      "asymptotic similarity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}