{
  "id": "0912.2457",
  "version": "v1",
  "published": "2009-12-12T22:28:42.000Z",
  "updated": "2009-12-12T22:28:42.000Z",
  "title": "A $d$-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process",
  "authors": [
    "Xavier Bardina Carles Rovira"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show how from an unique standard Poisson process we can build a family of processes that converges in law to a $d$-dimensional standard Brownian motion for any $d \\ge 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-12T22:28:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensional brownian motion",
      "one-dimensional poisson process",
      "weak limit",
      "unique standard poisson process",
      "dimensional standard brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.2457B"
    }
  }
}