{
  "id": "1505.01692",
  "version": "v1",
  "published": "2015-05-07T13:12:18.000Z",
  "updated": "2015-05-07T13:12:18.000Z",
  "title": "Rough flows",
  "authors": [
    "I. Bailleul",
    "S. Riedel"
  ],
  "comment": "48 pages",
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "We introduce in this work a concept of rough driver that somehow provides a rough path-like analogue of an enriched object associated with time-dependent vector fields. We use the machinery of approximate flows to build the integration theory of rough drivers and prove well-posedness results for rough differential equations on flows and continuity of the solution flow as a function of the generating rough driver. We show that the theory of semi-martingale stochastic flows developed in the 80's and early 90's fits nicely in this framework, and obtain as a consequence some strong approximation results for general semimartingale flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-07T13:12:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rough flows",
      "general semimartingale flows",
      "strong approximation results",
      "time-dependent vector fields",
      "rough differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150501692B"
    }
  }
}