{
  "id": "1006.4238",
  "version": "v1",
  "published": "2010-06-22T09:07:19.000Z",
  "updated": "2010-06-22T09:07:19.000Z",
  "title": "The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6",
  "authors": [
    "Ivan Nourdin",
    "Anthony Réveillac",
    "Jason Swanson"
  ],
  "comment": "45 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $B$ be a fractional Brownian motion with Hurst parameter $H=1/6$. It is known that the symmetric Stratonovich-style Riemann sums for $\\int g(B(s))\\,dB(s)$ do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of c\\`adl\\`ag functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary It\\^o integral with respect to a Brownian motion that is independent of $B$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-22T09:07:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional brownian motion",
      "weak stratonovich integral",
      "hurst parameter",
      "symmetric stratonovich-style riemann sums",
      "resulting stochastic integral satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.4238N"
    }
  }
}