{
  "id": "0705.1773",
  "version": "v2",
  "published": "2007-05-12T13:53:21.000Z",
  "updated": "2008-02-14T18:26:20.000Z",
  "title": "The rate of convergence of Euler approximations for solutions of stochastic differential equations driven by fractional Brownian motion",
  "authors": [
    "Yuliya Mishura",
    "Georgiy Shevchenko"
  ],
  "comment": "21 pages, (incorrect) weak convergence result removed, to appear in Stochastics",
  "journal": "Stochastics An International Journal of Probability and Stochastic Processes 80 (2008), 489-511",
  "doi": "10.1080/17442500802024892",
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index $H>1/2$ can be estimated by $O(\\delta^{2H-1})$ ($\\delta$ is the diameter of partition). For discrete-time approximations of Skorohod-type quasilinear equation driven by fBm we prove that the rate of convergence is $O(\\delta^H)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-14T18:26:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60G18"
    ],
    "keywords": [
      "stochastic differential equations driven",
      "fractional brownian motion",
      "euler approximations",
      "convergence",
      "skorohod-type quasilinear equation driven"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.1773M"
    }
  }
}