{
  "id": "0904.4519",
  "version": "v1",
  "published": "2009-04-29T01:40:03.000Z",
  "updated": "2009-04-29T01:40:03.000Z",
  "title": "On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion",
  "authors": [
    "Mingshang Hu",
    "Shige Peng"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a very simple and elementary proof of the existence of a weakly compact family of probability measures $\\{P_{\\theta}:\\theta \\in \\Theta \\}$ to represent an important sublinear expectation--G-expectation $\\mathbb{E}[\\cdot]$. We also give a concrete approximation of a bounded continuous function $X(\\omega)$ by an increasing sequence of cylinder functions $L_{ip}(\\Omega)$ in order to prove that $C_{b}(\\Omega)$ belongs to the $\\mathbb{E}[|\\cdot|]$-completion of the $L_{ip}(\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-29T01:40:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H05",
      "60H30",
      "60E05",
      "60E07",
      "62C05",
      "62D05"
    ],
    "keywords": [
      "g-brownian motion",
      "representation theorem",
      "g-expectations",
      "important sublinear expectation-g-expectation",
      "elementary proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.4519H"
    }
  }
}