{
  "id": "1407.0237",
  "version": "v1",
  "published": "2014-07-01T13:38:10.000Z",
  "updated": "2014-07-01T13:38:10.000Z",
  "title": "Bessel processes, the Brownian snake and super-Brownian motion",
  "authors": [
    "Jean-François Le Gall"
  ],
  "comment": "Submitted to the special volume of S\\'eminaire de Probabilit\\'es in memory of Marc Yor",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-01T13:38:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J68",
      "60J80"
    ],
    "keywords": [
      "super-brownian motion",
      "bessel processes",
      "minimal spatial position",
      "spine decomposition",
      "minimizing path"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0237L"
    }
  }
}