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

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  • Weina Wu

    (Nanjing University of Finance and Economics
    University of Bielefeld)

  • Jianliang Zhai

    (University of Science and Technology of China)

  • Jiahui Zhu

    (Zhejiang University of Technology)

Abstract

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 $$\mathbb {R}^d$$ 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

Suggested Citation

  • Weina Wu & Jianliang Zhai & Jiahui Zhu, 2025. "Large Deviations for Locally Monotone Stochastic Partial Differential Equations Driven by Lévy Noise," Journal of Theoretical Probability, Springer, vol. 38(4), pages 1-33, December.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:4:d:10.1007_s10959-025-01437-6
    DOI: 10.1007/s10959-025-01437-6
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    References listed on IDEAS

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    1. Cardon-Weber, Caroline, 1999. "Large deviations for a Burgers'-type SPDE," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 53-70, November.
    2. Budhiraja, Amarjit & Chen, Jiang & Dupuis, Paul, 2013. "Large deviations for stochastic partial differential equations driven by a Poisson random measure," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 523-560.
    3. Duan, Jinqiao & Millet, Annie, 2009. "Large deviations for the Boussinesq equations under random influences," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2052-2081, June.
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