{
  "id": "1108.1099",
  "version": "v2",
  "published": "2011-08-04T14:16:57.000Z",
  "updated": "2012-05-04T15:20:36.000Z",
  "title": "Convergence rates for the full Gaussian rough paths",
  "authors": [
    "Peter Friz",
    "Sebastian Riedel"
  ],
  "comment": "45 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "Under the key assumption of finite {\\rho}-variation, {\\rho}\\in[1,2), of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), {\\rho}=1 resp. {\\rho}=1/(2H), we recover and extend the respective results of [Hu--Nualart; Rough path analysis via fractional calculus; TAMS 361 (2009) 2689-2718] and [Deya--Neuenkirch--Tindel; A Milstein-type scheme without L\\'evy area terms for SDEs driven by fractional Brownian motion; AIHP (2011)]. In particular, we establish an a.s. rate k^{-(1/{\\rho}-1/2-{\\epsilon})}, any {\\epsilon}>0, for Wong-Zakai and Milstein-type approximations with mesh-size 1/k. When applied to fBM this answers a conjecture in the afore-mentioned references.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-04T15:20:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H35",
      "60H10",
      "60G15",
      "65C30"
    ],
    "keywords": [
      "full gaussian rough paths",
      "convergence rates",
      "fractional brownian motion",
      "rough path analysis",
      "levy area terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.1099F"
    }
  }
}