{
  "id": "1801.07574",
  "version": "v1",
  "published": "2018-01-23T14:37:23.000Z",
  "updated": "2018-01-23T14:37:23.000Z",
  "title": "Transfer Principle for nth Order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law",
  "authors": [
    "Tommi Sottinen",
    "Lauri Viitasaari"
  ],
  "comment": "20 pages, 20 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "The $n$th order fractional Brownian motion was introduced by Perrin et al. It is the (upto a multiplicative constant) unique self-similar Gaussian process with Hurst index $H \\in (n-1,n)$, having $n$th order stationary increments. We provide a transfer principle for the $n$th order fractional Brownian motion, i.e., we construct a Brownian motion from the $n$the order fractional Brownian motion and then represent the $n$the order fractional Brownian motion by using the Brownian motion in a non-anticipative way so that the filtrations of the $n$the order fractional Brownian motion and the associated Brownian motion coincide. By using this transfer principle, we provide the prediction formula for the $n$the order fractional Brownian motion and also a representation formula for all the Gaussian processes that are equivalent in law to the $n$th order fractional Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-23T14:37:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G15",
      "60G25",
      "60G35",
      "60H99"
    ],
    "keywords": [
      "nth order fractional brownian motion",
      "transfer principle",
      "prediction",
      "equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}