{
  "abstract": "We study a class of non-negative spatio-temporal random fields that exhibit self-exciting clustering, which we refer to as affine pure-jump Volterra fields. They are defined via stochastic integration of a Volterra kernel against a thinned Poisson random measure and the thinning is such that the field admits a representation as a stochastic integral of the same kernel, but against a random measure whose compensator has a density that is pointwise affine in the field itself. This representation leads to affine transform formulas characterizing the Laplace transform of functionals of the field up to the solution of a deterministic non-linear Volterra integral equation. Affine pure-jump Volterra random fields extend a non-negative finite-first-moment subclass of pure-jump affine Volterra processes to the random-field setting. The framework includes non-negative finite-variation ambit fields, marked Hawkes systems, and branching-type models as special cases, and we make these connections explicit through examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31102",
  "author_total": 2,
  "authors": [
    {
      "name": "Sven Karbach"
    },
    {
      "name": "Thomas K. Kloster"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2y43xcebwby9d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31102",
  "fulltext_url": null,
  "id": "2y43xcebwby9d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31102",
  "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"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7214578871",
  "pdf_url": "https://arxiv.org/pdf/2609.31102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2y43xcebwby9d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Affine pure-jump Volterra fields",
  "title_text": "Affine pure-jump Volterra fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/2y43xcebwby9d",
  "venue": "arXiv",
  "versions": []
}