{
  "id": "1510.04798",
  "version": "v1",
  "published": "2015-10-16T07:00:31.000Z",
  "updated": "2015-10-16T07:00:31.000Z",
  "title": "Independent random variables on Abelian groups with independent the sum and difference",
  "authors": [
    "G. M. Feldman"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let X be a second countable locally compact Abelian group. Let $\\xi_1, \\xi_2$ be independent random variables with values in the group X and distributions $\\mu_1, \\mu_2$ such that the sum $\\xi_1+\\xi_2$ and the difference $\\xi_1-\\xi_2$ are independent. Assuming that the connected component of zero of the group $X$ contains a finite number elements of order 2 we describe the possible distributions $\\mu_k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-16T07:00:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "independent random variables",
      "difference",
      "second countable locally compact abelian",
      "finite number elements",
      "countable locally compact abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151004798F"
    }
  }
}