{
  "abstract": "In this paper, we study the asymptotic behaviour for distribution of supercritical branching process in a Markovian environment with linear fractional offspring distributions. Phase transitions in the behaviour of the process is discovered, through investigating the strongly, intermediately and weakly supercritical cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04759",
  "author_total": 2,
  "authors": [
    {
      "name": "Yinna Ye"
    },
    {
      "name": "Quansheng Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0ym7xjvz89s7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04759",
  "fulltext_url": null,
  "id": "b0ym7xjvz89s7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04759",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7167639931",
  "pdf_url": "https://arxiv.org/pdf/2607.04759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0ym7xjvz89s7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2607.04759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Limit theorems for supercritical branching processes in Markovian environment with linear fractional offspring distributions",
  "title_text": "Limit theorems for supercritical branching processes in Markovian environment with linear fractional offspring distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/b0ym7xjvz89s7",
  "venue": "arXiv",
  "versions": []
}