{
  "id": "1703.03238",
  "version": "v1",
  "published": "2017-03-09T11:57:58.000Z",
  "updated": "2017-03-09T11:57:58.000Z",
  "title": "Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains",
  "authors": [
    "Yiqing Lin",
    "Abdoulaye Soumana Hima"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with $\\alpha$-H\\\"older continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected $G$-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by $G$-Brownian motion are investigated via a fixed-point argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-09T11:57:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "reflected stochastic differential equations driven",
      "brownian motion",
      "non-convex domains",
      "multi-dimensional reflected stochastic differential equations",
      "solving deterministic skorokhod problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}