Large Deviations for Locally Monotone Stochastic Partial Differential Equations Driven by Lévy Noise

• Published in: Journal of theoretical probability Vol. 38; no. 4
• Main Authors: Wu, Weina, Zhai, Jianliang, Zhu, Jiahui
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2025; Springer Nature B.V
• Subjects: Burgers equation; Deviation; Embedding; Laplace equation; Mathematics; Mathematics and Statistics; Newtonian fluids; Non Newtonian fluids; Partial differential equations; Probability Theory and Stochastic Processes; Statistics; Freidlin–Wentzell type large deviation principle; 35R60; 60F10; 35Q35; 60G51; stochastic partial differential equations; locally monotone; Lévy noise; 60H15
• ISSN: 0894-9840; 1572-9230
• DOI: 10.1007/s10959-025-01437-6

We establish a Freidlin–Wentzell type large deviation principle (LDP) for a class of SPDEs with locally monotone coefficients driven by Lévy noise. Our results improve the work on this topic (Bernoulli, 2018), because we drop the compactness embedding assumptions, and we also make the conditions for the coefficient of the noise term more specific and weaker. We utilize an improved sufficient criterion of Budhiraja, Chen, Dupuis, and Maroulas for functions of Poisson random measures. To remove the compactness embedding assumptions, we adopt a technical procedure introduced in SIAM J. Math. Anal., 2024, which includes the methods of time discretization, a cutoff argument, and relative entropy estimates of a sequence of probability measures. As an application, we derive, for the first time, the Freidlin–Wentzell-type LDPs for SPDEs driven by Lèvy noise in unbounded domains of R d , which are generally lack of compactness embedding properties. Such examples include the stochastic p-Laplace equation, stochastic Burgers-type equations, stochastic 2D Navier–Stokes equations, and stochastic equations of non-Newtonian fluids, among others