{
  "id": "1312.4632",
  "version": "v2",
  "published": "2013-12-17T04:03:56.000Z",
  "updated": "2016-05-11T17:48:40.000Z",
  "title": "On the Time for Brownian Motion to Visit Every Point on a Circle",
  "authors": [
    "Philip Ernst",
    "Larry Shepp"
  ],
  "comment": "8 pages, 1 figure",
  "journal": "Journal of Statistical Planning and Inference (2016): Volume 171, pages 130-134",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a Wiener process $W$ on a circle of circumference $L$. We prove the rather surprising result that the Laplace transform of the distribution of the first time, $\\theta_L$, when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-17T04:03:56.000Z",
      "abstract": "In this note, we find the distribution of times for which a Brownian motion has visited every point on a circle. We hope that this note will lead to finding the distribution of the covering time for Brownian motion for a variety of random graph structures.",
      "comment": "7 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-05-11T17:48:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60G15"
    ],
    "keywords": [
      "brownian motion",
      "random graph structures",
      "distribution",
      "covering time"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4632E"
    }
  }
}