{
  "id": "2006.03587",
  "version": "v1",
  "published": "2020-06-05T17:58:32.000Z",
  "updated": "2020-06-05T17:58:32.000Z",
  "title": "Diffusions on a space of interval partitions: construction from Bertoin's ${\\tt BES}_0(d)$, $d\\in(0,1)$",
  "authors": [
    "Matthias Winkel"
  ],
  "comment": "12 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In 1990, Bertoin constructed a measure-valued Markov process in the framework of a Bessel process of dimension between 0 and 1. In the present paper, we represent this process in a space of interval partitions. We show that this is a member of a class of interval partition diffusions introduced recently and independently by Forman, Pal, Rizzolo and Winkel using a completely different construction from spectrally positive stable L\\'evy processes with index between 1 and 2 and with jumps marked by squared Bessel excursions of a corresponding dimension between $-2$ and 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-05T17:58:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J60",
      "60J80",
      "60G18",
      "60G55"
    ],
    "keywords": [
      "construction",
      "interval partition diffusions",
      "measure-valued markov process",
      "squared bessel excursions",
      "bessel process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}