{
  "id": "1007.0687",
  "version": "v1",
  "published": "2010-07-05T14:14:00.000Z",
  "updated": "2010-07-05T14:14:00.000Z",
  "title": "Type A Distributions: Infinitely Divisible Distributions Related to Arcsine Density",
  "authors": [
    "Makoto Maejima",
    "Victor Perez-Abreu",
    "Ken-iti Sato"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Two transformations $\\mathcal{A}_{1}$ and $\\mathcal{A}_{2}$ of L\\'{e}vy measures on $\\mathbb{R}^{d}$ based on the arcsine density are studied and their relation to general Upsilon transformations is considered. The domains of definition of $\\mathcal{A}_{1}$ and $\\mathcal{A}_{2}$ are determined and it is shown that they have the same range. Infinitely divisible distributions on $\\mathbb{R}^{d}$ with L\\'{e}vy measures being in the common range are called type $A$ distributions and expressed as the law of a stochastic integral $\\int_0^1\\cos (2^{-1}\\pi t)dX_t$ with respect to L\\'{e}vy process $\\{X_t\\}$. \\ This new class includes as a proper subclass the Jurek class of distributions. It is shown that generalized type $G$ distributions are the image of type $A$ distributions under a mapping defined by an appropriate stochastic integral. $\\mathcal{A}_{2}$ is identified as an Upsilon transformation, while $\\mathcal{A}_{1}$ is shown to be not.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-05T14:14:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E07"
    ],
    "keywords": [
      "infinitely divisible distributions",
      "arcsine density",
      "appropriate stochastic integral",
      "general upsilon transformations",
      "jurek class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0687M"
    }
  }
}