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Large and Moderate Deviations Principles and Central Limit Theorem for the Stochastic 3D Primitive Equations with Gradient-Dependent Noise

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  • Jakub Slavík

    (The Czech Academy of Sciences)

Abstract

We establish the large deviations principle (LDP), the moderate deviations principle (MDP), and an almost sure version of the central limit theorem (CLT) for the stochastic 3D viscous primitive equations driven by multiplicative white noise allowing dependence on the spatial gradient of velocity with initial data in $$H^2$$ H 2 . We establish the LDP using the weak convergence approach by Budjihara and Dupuis and a uniform version of the stochastic Gronwall lemma. The result corrects a minor technical issue in Dong et al. (J Differ Equ 263(5):3110–3146, 2017) and establishes the result for a more general noise. The MDP is established by a similar argument.

Suggested Citation

  • Jakub Slavík, 2022. "Large and Moderate Deviations Principles and Central Limit Theorem for the Stochastic 3D Primitive Equations with Gradient-Dependent Noise," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1736-1781, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01125-1
    DOI: 10.1007/s10959-021-01125-1
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    1. Liu, Wei & Röckner, Michael & Zhu, Xiang-Chan, 2013. "Large deviation principles for the stochastic quasi-geostrophic equations," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3299-3327.
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