{
  "id": "2006.01597",
  "version": "v1",
  "published": "2020-06-01T14:19:55.000Z",
  "updated": "2020-06-01T14:19:55.000Z",
  "title": "A direct construction of the Standard Brownian Motion",
  "authors": [
    "Lo Gane Samb",
    "Niang Aladji Babacar",
    "Sangare Harouna"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note, we combine the two approaches of Billingsley (1998) and Cs\\H{o}rg\\H{o} and R\\'ev\\'esz (1980), to provide a detailed sequential and descriptive for creating s standard Brownian motion, from a Brownian motion whose time space is the class of non-negative dyadic numbers. By adding the proof of Etemadi's inequality to text, it becomes self-readable and serves as an independent source for researches and professors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-01T14:19:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Gxx",
      "60G15",
      "60G17"
    ],
    "keywords": [
      "standard brownian motion",
      "direct construction",
      "time space",
      "non-negative dyadic numbers",
      "etemadis inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}