{
  "id": "2312.08637",
  "version": "v1",
  "published": "2023-12-14T03:38:06.000Z",
  "updated": "2023-12-14T03:38:06.000Z",
  "title": "Arithmetic of a certain semigroup of probability distributions on the group $\\mathbb{R}\\times \\mathbb{Z}(2)$",
  "authors": [
    "Gennadiy Feldman"
  ],
  "comment": "11 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a certain convolution semigroup $\\Theta$ of probability distributions on the group $\\mathbb{R}\\times \\mathbb{Z}(2)$, where $\\mathbb{R}$ is the group of real numbers and $\\mathbb{Z}(2)$ is the additive group of the integers modulo 2. This semigroup appeared in connection with the study of a characterization problem of mathematical statistics on $a$-adic solenoids containing an element of order 2. We answer the questions that arise in the study of arithmetic of the semigroup $\\Theta$. Namely, we describe the class of infinitely divisible distributions, the class of indecomposable distributions, and the class of distributions which have no indecomposable factors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-14T03:38:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B15"
    ],
    "keywords": [
      "probability distributions",
      "arithmetic",
      "convolution semigroup",
      "real numbers",
      "characterization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}