{
  "id": "1508.00361",
  "version": "v1",
  "published": "2015-08-03T09:59:11.000Z",
  "updated": "2015-08-03T09:59:11.000Z",
  "title": "Stochastic equation of fragmentation and branching processes related to avalanches",
  "authors": [
    "Lucian Beznea",
    "Madalina Deaconu",
    "Oana Lupascu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a stochastic model for the fragmentation phase of a snow avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentation sizes introduced by J. Bertoin. A fractal property of this process is emphasized. We also establish a specific stochastic equation of fragmentation. It turns out that specific branching Markov processes on finite configurations of particles with sizes bigger than a strictly positive threshold are convenient for describing the continuous time evolution of the number of the resulting fragments. The results are obtained by combining analytic and probabilistic potential theoretical tools.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-03T09:59:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60J45",
      "60J35",
      "60K35"
    ],
    "keywords": [
      "branching processes",
      "specific stochastic equation",
      "specific branching markov processes",
      "probabilistic potential theoretical tools",
      "fractal property"
    ],
    "publication": {
      "doi": "10.1007/s10955-015-1432-5",
      "journal": "Journal of Statistical Physics",
      "year": 2016,
      "month": "Feb",
      "volume": 162,
      "number": 4,
      "pages": 824
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016JSP...162..824B"
    }
  }
}