{
  "abstract": "In this paper, we study the asymptotic behavior of the extremal process of a standard one-dimensional branching Brownian motion (BBM) with drift $-ρ>-\\sqrt2$ and absorbing barrier at level $-x$. We prove that the two-dimensional point process, with first component being the extremal process of the BBM and the second component being the running minimum of the BBM with drift, converges weakly to a decorated Poisson point process (DPPP) on $\\mathbb{R} \\times [0, \\infty)$. This framework allows us to supply a common limit coupling of the extremal processes for different barrier levels and to explicitly derive the limit, as $t\\to\\infty$, of the extremal process of the killed BBM killed at level $-x$, demonstrating that the double limit, when $t\\to\\infty$ first and then $x\\to\\infty$, of the extremal process of the BBM killed at level $-x$ coincides with the limit of the extremal process of (un-killed) BBM.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28989",
  "author_total": 3,
  "authors": [
    {
      "name": "Yan-Xia Ren"
    },
    {
      "name": "Renming Song"
    },
    {
      "name": "Fan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmezzs1rg9mda.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28989",
  "fulltext_url": null,
  "id": "dmezzs1rg9mda",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28989",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7214405681",
  "pdf_url": "https://arxiv.org/pdf/2609.28989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmezzs1rg9mda.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2609.28989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28989"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "From killed BBM with drift to BBM: the extremal process",
  "title_text": "From killed BBM with drift to BBM: the extremal process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/dmezzs1rg9mda",
  "venue": "arXiv",
  "versions": []
}