{
  "id": "math/0604315",
  "version": "v4",
  "published": "2006-04-13T15:06:28.000Z",
  "updated": "2007-10-18T11:11:12.000Z",
  "title": "Stochastic derivatives for fractional diffusions",
  "authors": [
    "Sébastien Darses",
    "Ivan Nourdin"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/009117906000001169 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2007, Vol. 35, No. 5, 1998-2020",
  "doi": "10.1214/009117906000001169",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given $\\sigma$-field $\\mathcal{Q}$. In our framework, we recall well-known results about Markov--Wiener diffusions. We then focus mainly on the case where $X$ is a fractional diffusion and where $\\mathcal{Q}$ is the past, the future or the present of $X$. We treat some crucial examples and our main result is the existence of stochastic derivatives with respect to the present of $X$ when $X$ solves a stochastic differential equation driven by a fractional Brownian motion with Hurst index $H>1/2$. We give explicit formulas.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-10-18T11:11:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G07",
      "60G15",
      "60G17",
      "60H07"
    ],
    "keywords": [
      "stochastic derivatives",
      "fractional diffusion",
      "stochastic differential equation driven",
      "fractional brownian motion",
      "recall well-known results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4315D"
    }
  }
}