{
  "id": "0707.0313",
  "version": "v1",
  "published": "2007-07-02T20:39:04.000Z",
  "updated": "2007-07-02T20:39:04.000Z",
  "title": "Differential Equations Driven by Gaussian Signals I",
  "authors": [
    "Peter Friz",
    "Nicolas Victoir"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider multi-dimensional Gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of stochastic area(s). Gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful - yet conceptually simple - framework in which to analysize differential equations driven by Gaussian signals in the rough paths sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-02T20:39:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60H99"
    ],
    "keywords": [
      "gaussian signals",
      "rough paths sense",
      "analysize differential equations driven",
      "strong approximation results",
      "multi-dimensional gaussian processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.0313F"
    }
  }
}