{
  "id": "0809.2958",
  "version": "v1",
  "published": "2008-09-17T16:32:18.000Z",
  "updated": "2008-09-17T16:32:18.000Z",
  "title": "Strong Law of Large Numbers for Fragmentation Processes",
  "authors": [
    "S. C. Harris",
    "R. Knobloch",
    "A. E. Kyprianou"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In the spirit of a classical results for Crump-Mode-Jagers processes, we prove a strong law of large numbers for homogenous fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than $\\eta$ for $1\\geq \\eta >0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-17T16:32:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60G09"
    ],
    "keywords": [
      "large numbers",
      "strong law",
      "self-similar fragmentation processes",
      "homogenous fragmentation processes",
      "crump-mode-jagers processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2958H"
    }
  }
}