{
  "id": "1701.03002",
  "version": "v1",
  "published": "2017-01-11T15:05:00.000Z",
  "updated": "2017-01-11T15:05:00.000Z",
  "title": "A support and density theorem for Markovian rough paths",
  "authors": [
    "Ilya Chevyrev",
    "Marcel Ogrodnik"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish two results concerning a class of geometric rough paths $\\mathbf{X}$ which arise as Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support theorem for $\\mathbf{X}$ in $\\alpha$-H\\\"older rough path topology for all $\\alpha \\in (0,1/2)$, which answers in the positive a conjecture of Friz-Victoir (2010). The second is a H\\\"ormander-type theorem for the existence of a density of a rough differential equation driven by $\\mathbf{X}$, the proof of which is based on analysis of (non-symmetric) Dirichlet forms on manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-11T15:05:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60G17"
    ],
    "keywords": [
      "markovian rough paths",
      "density theorem",
      "rough differential equation driven",
      "geometric rough paths",
      "uniformly subelliptic dirichlet forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}