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On conservativity of multitype continuous-state branching processes — arXiv:2610.23649

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.23649
License (as archived): CC0-1.0
Archived: 2026-10-19T09:38:05.771Z
SHA-256 of the archived text: 21373191e5b4b110e737dd1df2395dd64ca3c65f545c8c6b5238b75465a3a918
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How to cite

On conservativity of multitype continuous-state branching processes — arXiv:2610.23649 — arXiv (en), https://arxiv.org/abs/2610.23649 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_20e4e5d160ff (Metraipolis archive dc_20e4e5d160ff, sha256 21373191e5b4b110e737dd1df2395dd64ca3c65f545c8c6b5238b75465a3a918)

BibTeX

@misc{dc20e4e5d160ff,
  title = {On conservativity of multitype continuous-state branching processes — arXiv:2610.23649},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.23649},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_20e4e5d160ff; sha256 21373191e5b4b110e737dd1df2395dd64ca3c65f545c8c6b5238b75465a3a918},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.23649. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In [4], Grey gives a condition on the branching mechanism $\psi$ of a continuous- state branching process Z ensuring that the process is conservative. This condition is obtained from the expression of the solution of the differential equation satisfied by the Laplace exponent of Z. In higher dimensions, it is generally no longer possible to make this solution explicit and very few conditions ensuring the conservativity of the process are known. In this paper, we provide necessary conditions and sufficient conditions for conservativity. For dimension 2, when types cannot regenerate themselves, we give a necessary and sufficient condition and we invert the Lamperti representation of the multitype branching process.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.23649 — 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 2026-10-19T09:34:14.703Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).