{
  "id": "1601.03535",
  "version": "v1",
  "published": "2016-01-14T10:11:39.000Z",
  "updated": "2016-01-14T10:11:39.000Z",
  "title": "Viability for Rough Differential Equations",
  "authors": [
    "Laure Coutin",
    "Nicolas Marie"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In 1990, in It\\^o stochastic calculus framework, Aubin and DaPrato established a necessary and sufficient condition of invariance of a nonempty compact or convex subset $C$ of $\\mathbb R^d$ ($d\\in\\mathbb N^*$) for stochastic differential equations driven by a Brownian motion. In Lyons rough paths framework, this paper deals with an extension of Aubin and DaPrato results to rough differential equations. A comparison theorem is provided, and the special case of differential equations driven by a fractional Brownian motion is detailed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-14T10:11:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10"
    ],
    "keywords": [
      "rough differential equations",
      "lyons rough paths framework",
      "stochastic differential equations driven",
      "fractional brownian motion",
      "stochastic calculus framework"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}