{
  "id": "1801.01546",
  "version": "v1",
  "published": "2017-12-31T21:28:05.000Z",
  "updated": "2017-12-31T21:28:05.000Z",
  "title": "Characterization of distributions of $Q$-independent random variables on locally compact Abelian groups",
  "authors": [
    "Margaryta Myronyuk"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1703.06484",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $X$ be a second countable locally compact Abelian group. We prove some group analogues of the Skitovich--Darmois, Heyde and Kac--Bernstein characterisation theorems for $Q$-independent random variables taking values in the group $X$. The proofs of these theorems are reduced to solving some functional equations on the character group of the group $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-31T21:28:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B15",
      "62E10",
      "43A35"
    ],
    "keywords": [
      "independent random variables",
      "characterization",
      "distributions",
      "kac-bernstein characterisation theorems",
      "countable locally compact abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}