{
  "id": "1205.4562",
  "version": "v1",
  "published": "2012-05-21T11:21:21.000Z",
  "updated": "2012-05-21T11:21:21.000Z",
  "title": "Rate of convergence for discretization of integrals with respect to Fractional Brownian motion",
  "authors": [
    "Lauri Viitasaari",
    "Ehsan Azmoodeh"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, an uniform discretization of stochastic integrals $\\int_{0}^{1} f'_-(B_t)\\ud B_t$, with respect to fractional Brownian motion with Hurst parameter $H \\in (1/2,1)$, for a large class of convex functions $f$ is considered. In Statistics & Decisions, 27, 129-143, for any convex function $f$, the almost sure convergence of uniform discretization to such stochastic integral is proved. Here we prove $L^r$- convergence of uniform discretization to stochastic integral. In addition, we obtain a rate of convergence. It turns out that the rate of convergence can be brought as closely as possible to $H - 1/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-21T11:21:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60H05",
      "41A25"
    ],
    "keywords": [
      "fractional brownian motion",
      "stochastic integral",
      "uniform discretization",
      "convex function",
      "large class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.4562V"
    }
  }
}