{
  "id": "0708.3730",
  "version": "v1",
  "published": "2007-08-28T08:43:09.000Z",
  "updated": "2007-08-28T08:43:09.000Z",
  "title": "Densities for Rough Differential Equations under Hoermander's Condition",
  "authors": [
    "Thomas Cass",
    "Peter Friz"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider stochastic differential equations dY=V(Y)dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Y(t) admits a density for t in (0,T] provided (i) the vector fields V=(V_1,...,V_d) satisfy Hoermander's condition and (ii) the Gaussian driving signal X satisfies certain conditions. Examples of driving signals include fractional Brownian motion with Hurst parameter H>1/4, the Brownian Bridge returning to zero after time T and the Ornstein-Uhlenbeck process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-28T08:43:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60G17"
    ],
    "keywords": [
      "rough differential equations",
      "rough path sense",
      "fractional brownian motion",
      "satisfy hoermanders condition",
      "multidimensional gaussian process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3730C"
    }
  }
}