{
  "id": "1910.04243",
  "version": "v1",
  "published": "2019-10-09T20:39:42.000Z",
  "updated": "2019-10-09T20:39:42.000Z",
  "title": "Remarks on asymptotic independence",
  "authors": [
    "Youri Davydov",
    "Svyatoslav Novikov"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we introduce 5 natural definitions (AI-0) - (AI-4) of asymptotic independence (AI) of two sequences ($X_n$), ($Y_n$) of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak dependence. In particular, the case of tight sequences is considered in detail. Finally, in order to clarify the relationships between AI-0 - AI-4, we provide some counterexamples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-09T20:39:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F99",
      "60G97",
      "60B10",
      "60B99"
    ],
    "keywords": [
      "asymptotic independence",
      "tight sequences",
      "weak dependence",
      "natural definitions",
      "simple connections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}