{
  "id": "1712.08279",
  "version": "v1",
  "published": "2017-12-22T02:10:07.000Z",
  "updated": "2017-12-22T02:10:07.000Z",
  "title": "Three series theorem for independent random variables under sub-linear expectations with applications",
  "authors": [
    "Jiapan Xu",
    "Lixin Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we give a theorem about the convergence of a random series and establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-22T02:10:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15"
    ],
    "keywords": [
      "sub-linear expectation",
      "independent random variables",
      "series theorem",
      "identically distributed random variables",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}