{
  "id": "math/0210272",
  "version": "v1",
  "published": "2002-10-17T17:36:08.000Z",
  "updated": "2002-10-17T17:36:08.000Z",
  "title": "A simple construction of the Fractional Brownian motion",
  "authors": [
    "Enriquez Nathanael"
  ],
  "comment": "15 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work we introduce correlated random walks on $\\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is the fractional Brownian motion. We have to use two radically different models for both cases ${1\\over2}\\leq H<1$ and $0<H<{1\\over2}$. This result provides an algorithm for the simulation of the fractional Brownian motion, which appears to be quite efficient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-17T17:36:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "60G15",
      "60G17",
      "60K37"
    ],
    "keywords": [
      "fractional brownian motion",
      "simple construction",
      "discrete gaussian process",
      "correlated random walks",
      "large number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10272N"
    }
  }
}