{
  "id": "1711.10649",
  "version": "v1",
  "published": "2017-11-29T02:32:10.000Z",
  "updated": "2017-11-29T02:32:10.000Z",
  "title": "Limit theorems with rate of convergence under sublinear expectations",
  "authors": [
    "Xiao Fang",
    "Shige Peng",
    "Qi-Man Shao",
    "Yongsheng Song"
  ],
  "comment": "31 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Under the sublinear expectation $\\mathbb{E}[\\cdot]:=\\sup_{\\theta\\in \\Theta} E_\\theta[\\cdot]$ for a given set of linear expectations $\\{E_\\theta: \\theta\\in \\Theta\\}$, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the $G$-normal distribution, which was used as the limit in Peng (2007)'s central limit theorem, in a probability space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-29T02:32:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05"
    ],
    "keywords": [
      "sublinear expectation",
      "central limit theorem",
      "convergence",
      "large numbers",
      "related statistical inference problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}