{
  "id": "1212.6353",
  "version": "v1",
  "published": "2012-12-27T11:43:13.000Z",
  "updated": "2012-12-27T11:43:13.000Z",
  "title": "Integral with respect to the $G$-Brownian local time",
  "authors": [
    "Litan Yan",
    "Xichao Sun",
    "Bo Gao"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "Let ${\\mathscr L}$ be the local time of $G$-Brownian motion $B$. In this paper, we prove the existence of the quadratic covariation $<f(B),B>_{t}$ and the integral $\\int_{\\mathbb R}f(x){\\mathscr L}(dx,t)$. Moreover, a sublinear version of the Bouleau-Yor identity $$ \\int_{\\mathbb R}f(x){\\mathscr L}(dx,t)=-<f(B),B>_{t} $$ is showed to hold under some suitable conditions. These allow us to write the It\\^o's formula for $C^1$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-27T11:43:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G05",
      "60G20",
      "60H05"
    ],
    "keywords": [
      "brownian local time",
      "brownian motion",
      "bouleau-yor identity",
      "sublinear version",
      "quadratic covariation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.6353Y"
    }
  }
}