{
  "abstract": "We study the asymptotic behavior of a sequence of Galton-Watson processes with inhomogeneous immigration when the limit of the means of the offspring distributions is equal to 1. Under a growth condition on the variances of the offspring distributions, assuming the locally uniform convergence of the expectation functions of properly scaled immigration processes towards a càdlàg function, and the locally uniform convergence of the mean absolute deviation functions of the scaled immigration processes in question towards zero, we establish a functional limit theorem for the sequence of Galton-Watson processes with inhomogeneous immigration in question towards a deterministic limit process. We also provide some applications, among others, we show that a recent result of Rahimov and Sharipov (2024) on a functional limit theorem for a sequence of nearly critical Galton-Watson processes with dependent immigration can be recovered using our result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39771",
  "author_total": 2,
  "authors": [
    {
      "name": "Matyas Barczy"
    },
    {
      "name": "Dániel Bezdány"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e5vhk2m702awf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39771",
  "fulltext_url": null,
  "id": "e5vhk2m702awf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39771",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39771",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e5vhk2m702awf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39771"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Functional limit theorems for Galton-Watson processes with inhomogeneous immigration towards a deterministic limit function",
  "title_text": "Functional limit theorems for Galton-Watson processes with inhomogeneous immigration towards a deterministic limit function",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/e5vhk2m702awf",
  "venue": "arXiv",
  "versions": []
}