{
  "annotation_id": "76f0600b-447b-44e3-8d36-944e62dcf762",
  "date_created": "2026-02-17T05:53:08.508000Z",
  "date_modified": "2026-02-17T05:53:08.508000Z",
  "file_hash": "4df305eb71add239c9070075d200f5bdafc2c3a429a466d43790732d0bebc41a",
  "private": false,
  "record": {
    "abstract": "In this short note, we provide an explicit sufficient condition for non-explosion of Crump--Mode--Jagers branching processes with pure birth reproduction. It shows that the standard sufficient condition for explosion, namely the convergence of the series of reciprocals of the birth rates, is -- at least for rate sequences without excessive oscillations -- remarkably close to being necessary. At the same time, it is not necessary in full generality: we construct a counterexample which also yields a general preferential attachment tree without fitness with an infinite path and no vertices of infinite degree, thereby answering an open question previously raised in the literature.",
    "arxiv_id": "2601.06850",
    "authors": [
      "Oleksii Galganov",
      "Andrii Ilienko"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Explosion and non-explosion in pure birth Crump--Mode--Jagers branching processes",
    "url": "https://arxiv.org/abs/2601.06850",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2ad3ae5f-53b3-4a72-a62f-914d7b0401f7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}