{
  "id": "1112.0452",
  "version": "v1",
  "published": "2011-12-02T12:52:34.000Z",
  "updated": "2011-12-02T12:52:34.000Z",
  "title": "Inversion of signature for paths of bounded variation",
  "authors": [
    "Terry Lyons",
    "Weijun Xu"
  ],
  "categories": [
    "math.CA",
    "math.PR"
  ],
  "abstract": "We develop two methods to reconstruct a path of bounded variation from its signature. The first method gives a simple and explicit expression of any axis path in terms of its signature, but it does not apply directlty to more general ones. The second method, based on an approximation scheme, recovers any tree-reduced path from its signature as the limit of a uniformly convergent sequence of lattice paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-02T12:52:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded variation",
      "uniformly convergent sequence",
      "first method",
      "approximation scheme",
      "second method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.0452L"
    }
  }
}