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arXiv · 2511.23420

Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise

Raluca M. Balan·Juan J. Jiménez·Lluís Quer-Sardanyons
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Abstract

In this article, we study the global well-posedness of hyperbolic SPDEs on a bounded domain in $\mathbb{R}^d$, driven by a space-time Lévy white noise, when the drift and diffusion coefficients are locally Lipschitz and have linear growth. The equations are driven by two types of space-time Lévy noise: (i) a finite-variance Lévy white noise; or (ii) a symmetric Lévy basis that may have infinite variance. A typical example of noise of the second type is the symmetric $α$-stable (S$α$S) random measure with $α\in (0,2)$.

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Raluca M. Balan, Juan J. Jiménez, Lluís Quer-Sardanyons. 2025-12-13. Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise. https://arxiv.org/abs/2511.23420

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