{
  "abstract": "Aldous' criterion provides a stopping-time characterisation of tightness in Skorokhod's $J_1$ topology and is one of the standard tools for proving functional limit theorems. For the weaker $M_1$ topology, where limiting jumps can be approximated by clustered jumps or steep continuous motion, no analogous characterisation has been available and tightness classically requires controlling a global oscillation modulus over all nearby triples of times. We prove such an Aldous-type characterisation of $M_1$ tightness, replacing the global modulus condition by local estimates at stopping times ruling out rapid reversals after a large excursion. Together with the standard compact containment and boundary conditions, these estimates are both necessary and sufficient for $M_1$ tightness. As a consequence, we derive tractable and general sufficient conditions for additive functionals of strong Markov processes. They reduce the verification of $M_1$ tightness to short-time estimates for the processes restarted from its state at suitable stopping times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27900",
  "author_total": 2,
  "authors": [
    {
      "name": "Grégoire Szymanski"
    },
    {
      "name": "Fabrice Wunderlich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eagcdad2hbxbq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27900",
  "fulltext_url": null,
  "id": "eagcdad2hbxbq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27900",
  "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.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223148887",
  "pdf_url": "https://arxiv.org/pdf/2610.27900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eagcdad2hbxbq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "An Aldous-type tightness characterisation for the $M_1$ topology: replacing global modulus control by local control at stopping times",
  "title_text": "An Aldous-type tightness characterisation for the M_1 topology: replacing global modulus control by local control at stopping times",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/eagcdad2hbxbq",
  "venue": "arXiv",
  "versions": []
}