{
  "id": "math/0304134",
  "version": "v2",
  "published": "2003-04-10T07:45:26.000Z",
  "updated": "2004-03-09T20:27:29.000Z",
  "title": "Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion",
  "authors": [
    "Martin Hairer"
  ],
  "comment": "49 pages, 8 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\\in(0,1)$. A general framework is constructed to make precise the notions of ``invariant measure'' and ``stationary state'' for such a system. We then prove under rather weak dissipativity conditions that such an SDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution towards the stationary one is (at least) algebraic. A lower bound on the exponent is also given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-09T20:27:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60G10",
      "37H10"
    ],
    "keywords": [
      "stochastic differential equations driven",
      "ergodicity",
      "non-degenerate additive fractional brownian motion",
      "arbitrary hurst parameter",
      "stationary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4134H"
    }
  }
}