{
  "id": "1509.00003",
  "version": "v1",
  "published": "2015-08-31T20:00:22.000Z",
  "updated": "2015-08-31T20:00:22.000Z",
  "title": "LAN property for stochastic differential equations with additive fractional noise and continuous time observation",
  "authors": [
    "Eulalia Nualart",
    "Samy Tindel"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a stochastic differential equation with additive fractional noise of Hurst parameter $H>1/2$, and a non-linear drift depending on an unknown parameter. We show the Local Asymptotic Normality property (LAN) of this parametric model with rate $\\sqrt{\\tau}$ as $\\tau\\rightarrow \\infty$, when the solution is observed continuously on the time interval $[0,\\tau]$. The proof uses ergodic properties of the equation and a Poincar\\'e type inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-31T20:00:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic differential equation",
      "additive fractional noise",
      "continuous time observation",
      "lan property",
      "local asymptotic normality property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}