{
  "id": "2307.06493",
  "version": "v1",
  "published": "2023-07-12T23:53:54.000Z",
  "updated": "2023-07-12T23:53:54.000Z",
  "title": "Bounded Bessel Processes and Ferrari-Spohn Diffusions",
  "authors": [
    "Matthew Lerner-Brecher"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a new diffusion process which arises as the $n\\to\\infty$ limit of a Bessel process of dimension $d \\ge 2$ conditioned upon remaining bounded below one until time $n$. In addition to being interesting in its own right, we argue that the resulting diffusion process is a natural hard edge counterpart to the Ferrari-Spohn diffusion of arXiv:math/0308242. In particular, we show that the generator of our new diffusion has the same relation to the Sturm-Liouville problem for the Bessel operator that the Ferrari-Spohn diffusion does to the corresponding problem for the Airy operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-12T23:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "34B24"
    ],
    "keywords": [
      "ferrari-spohn diffusion",
      "bounded bessel processes",
      "natural hard edge counterpart",
      "airy operator",
      "bessel operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}