Metraipolis › archive › dc_fb33905fffff

Affine pure-jump Volterra fields — arXiv:2609.31102

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.31102
License (as archived): CC0-1.0
Archived: 2026-10-08T02:57:36.738Z
SHA-256 of the archived text: 14ddd23355fd9e5bbdff38d0533cadec63613feb48d23db6c9eab31d680f19bd
Stable URL of this page: https://metraipolis.com/documento/dc_fb33905fffff

How to cite

Affine pure-jump Volterra fields — arXiv:2609.31102 — arXiv (en), https://arxiv.org/abs/2609.31102 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fb33905fffff (Metraipolis archive dc_fb33905fffff, sha256 14ddd23355fd9e5bbdff38d0533cadec63613feb48d23db6c9eab31d680f19bd)

BibTeX

@misc{dcfb33905fffff,
  title = {Affine pure-jump Volterra fields — arXiv:2609.31102},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.31102},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fb33905fffff; sha256 14ddd23355fd9e5bbdff38d0533cadec63613feb48d23db6c9eab31d680f19bd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.31102. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-28 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.31102 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T02:27:13.363Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).