Metraipolis › archive › dc_2c98625f2b7f

Unique Ergodicity for Strongly Damped Stochastic Wave Equations under Finite-Rank Pure-Jump Lévy Forcing — arXiv:2610.09521

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.09521
License (as archived): CC0-1.0
Archived: 2026-10-08T12:43:09.353Z
SHA-256 of the archived text: 90e8fab9691c7892c740d58aa0f684d988a5a19b3190c3b060dae7c9917f367d
Stable URL of this page: https://metraipolis.com/documento/dc_2c98625f2b7f

How to cite

Unique Ergodicity for Strongly Damped Stochastic Wave Equations under Finite-Rank Pure-Jump Lévy Forcing — arXiv:2610.09521 — arXiv (en), https://arxiv.org/abs/2610.09521 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2c98625f2b7f (Metraipolis archive dc_2c98625f2b7f, sha256 90e8fab9691c7892c740d58aa0f684d988a5a19b3190c3b060dae7c9917f367d)

BibTeX

@misc{dc2c98625f2b7f,
  title = {Unique Ergodicity for Strongly Damped Stochastic Wave Equations under Finite-Rank Pure-Jump Lévy Forcing — arXiv:2610.09521},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.09521},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2c98625f2b7f; sha256 90e8fab9691c7892c740d58aa0f684d988a5a19b3190c3b060dae7c9917f367d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.09521. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study a strongly damped stochastic wave equation on the three-dimensional torus driven by finite-rank pure-jump Lévy noise obtained from subordinated Brownian motion. Lyapunov estimates and an asymptotic compactness decomposition yield invariant measures, and a small-noise event gives weak irreducibility. To prove uniqueness, we combine conditional Malliavin calculus with terminal observability and estimates for the full variational flow starting from high modes. A control constructed on alternating stopping blocks yields the e-property under a fixed-rank balance condition involving high-mode decay, spectral leakage, and the random clock. Consequently, the invariant measure is unique and ergodic, and the Cesàro averages of the transition laws from every initial state converge weakly to it. We verify this condition for sufficiently small positive cubic coefficients at each fixed forcing operator of sufficiently large rank. Under a separate explicit smallness condition, synchronous coupling proves the e-property and weak convergence of the transition laws, without a lower bound on the forcing rank.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR) ; Dynamical Systems (math.DS).
Pagina del lavoro: https://arxiv.org/abs/2610.09521 — 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 2026-10-08T12:16:30.198Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).