{
  "id": "1806.02265",
  "version": "v1",
  "published": "2018-06-06T15:58:19.000Z",
  "updated": "2018-06-06T15:58:19.000Z",
  "title": "BSDEs driven by $G$-Brownian motion with uniformly continuous generators",
  "authors": [
    "Falei Wang",
    "Guoqiang Zheng"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs). In fact, when the generators are Lipschitz continuous in $y$ and uniformly continuous in $z$, we construct the unique solution to such equations by monotone convergence argument. The comparison theorem and related Feynman-Kac formula are stated as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-06T15:58:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30"
    ],
    "keywords": [
      "brownian motion",
      "uniformly continuous generators",
      "stochastic differential equations driven",
      "bsdes driven",
      "backward stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}