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Finite Explosion for One-dimensional Lévy Driven SDEs and its Application to SPDEs — arXiv:2609.21954

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21954
License (as archived): CC0-1.0
Archived: 2026-10-10T02:07:21.752Z
SHA-256 of the archived text: c9a9806d3c3e766c130c1505aa5feaf7ff9c4b3bc31a1d753673f22342ebb2dd
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How to cite

Finite Explosion for One-dimensional Lévy Driven SDEs and its Application to SPDEs — arXiv:2609.21954 — arXiv (en), https://arxiv.org/abs/2609.21954 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cc1925eceef8 (Metraipolis archive dc_cc1925eceef8, sha256 c9a9806d3c3e766c130c1505aa5feaf7ff9c4b3bc31a1d753673f22342ebb2dd)

BibTeX

@misc{dccc1925eceef8,
  title = {Finite Explosion for One-dimensional Lévy Driven SDEs and its Application to SPDEs — arXiv:2609.21954},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21954},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cc1925eceef8; sha256 c9a9806d3c3e766c130c1505aa5feaf7ff9c4b3bc31a1d753673f22342ebb2dd},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21954. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study finite-time explosion to $-\infty$ for the one-dimensional stochastic differential equation \[ X_t^x=x-\int_0^t b(X_s^x)\,\dd s+L_t,\quad x\in\R, \] where $b$ is locally Lipschitz and $(L_t)_{t\ge0}$ is a pure-jump Lévy process. We give verifiable conditions involving Osgood-type integrability under which explosion occurs almost surely from every finite initial state. Under stronger tail conditions, we obtain a uniform bound on the mean explosion time. In particular, under suitable tail monotonicity, converse results make these criteria necessary and sufficient, and yield an explicit classification for Riccati drifts. As an application, we consider a semilinear parabolic stochastic partial differential equation (SPDE) with additive Lévy space--time white noise and homogeneous Dirichlet boundary conditions. We give explicit conditions on the nonlinearity and the Lévy measure under which every local weak solution defined up to explosion has an almost surely finite explosion time.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-21 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.21954 — 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 2026-10-10T01:47:50.209Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).