{
  "id": "math/0603199",
  "version": "v1",
  "published": "2006-03-08T20:52:27.000Z",
  "updated": "2006-03-08T20:52:27.000Z",
  "title": "Self-similarity and fractional Brownian motions on Lie groups",
  "authors": [
    "F. Baudoin",
    "L. Coutin"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this process has stationary increments and satisfies a local self-similar property. Furthermore the Lie groups for which this self-similar property is global are characterized. Finally, we prove an integration by parts formula on the path group space and deduce the existence of a density.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-08T20:52:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie group",
      "self-similarity",
      "stochastic differential equation driven",
      "linear fractional brownian motion",
      "local self-similar property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3199B"
    }
  }
}