{
  "id": "1001.3344",
  "version": "v1",
  "published": "2010-01-19T16:12:16.000Z",
  "updated": "2010-01-19T16:12:16.000Z",
  "title": "A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion",
  "authors": [
    "Aurélien Deya",
    "Andreas Neuenkirch",
    "Samy Tindel"
  ],
  "journal": "Annales de l'Institut Henri Poincar\\'e (B) Probabilit\\'es et Statistiques 48, 2 (2012) 518-550",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second order Taylor expansion, where the usual Levy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds for the discretisation of the Levy area terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-19T16:12:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H35",
      "60H07",
      "60H10",
      "65C30"
    ],
    "keywords": [
      "sdes driven",
      "milstein-type scheme",
      "usual levy area terms",
      "stochastic differential equations driven",
      "second order taylor expansion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012AnIHP..48..518D"
    }
  }
}