{
  "abstract": "We provide an event-level Hawkes microfoundation for a multitype inverse-Gaussian stochastic clock. We show that the event counts and integrated intensities of nearly critical multivariate linear Hawkes processes converge jointly to a multivariate pure-jump subordinator when reproduction delays have finite mean and immigration is balanced so that rare large families remain visible. The dependence among the limiting coordinates is inherited from microscopic cross-excitation, and the limit admits a Brownian additive-field first-passage representation. We call this process the multitype inverse-Gaussian subordinator. Its diagonal case consists of independent classical inverse-Gaussian subordinators, with the univariate model as a further special case. The square-root specialization recovers the inverse-Gaussian clock obtained at the boundary of hyper-rough square-root models by Abi Jaber--Attal--Rosenbaum (\\textit{Ann. Appl. Probab.} \\textbf{36}(4): 3635--3660, 2026). Our cluster proof exposes the underlying mechanism: finite-variance near-critical branching creates rare but macroscopic families, while their internal timing disappears on the observation scale, so each family becomes a jump. We also clarify the relation with the multivariate Hawkes scaling theory of Xu (arXiv:2412.14459): its diagonal-atom condition yields the diagonal specialization, whereas the genuinely coupled limit requires a separate uniqueness argument. In addition, under a common tilted-stability condition, we replace the high-intensity assumption in that theory by a weaker accumulated-activity condition and provide the Riccati identification needed when the potential has an atom. We strengthen convergence of the count and compensator and extend the scalar conclusion to finite-variance age-dependent branching clusters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10525",
  "author_total": 3,
  "authors": [
    {
      "name": "Yingli Wang"
    },
    {
      "name": "Wei Xu"
    },
    {
      "name": "Lingjiong Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/df24p90tprt52.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10525",
  "fulltext_url": null,
  "id": "df24p90tprt52",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10525",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-fin.MF"
    ],
    [
      "arxiv",
      "q-fin.TR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221058447",
  "pdf_url": "https://arxiv.org/pdf/2610.10525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/df24p90tprt52.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Hawkes Microfoundation for Multitype Inverse Gaussian Subordinators",
  "title_text": "A Hawkes Microfoundation for Multitype Inverse Gaussian Subordinators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/df24p90tprt52",
  "venue": "arXiv",
  "versions": []
}