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

Jakub Slavík ()
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Jakub Slavík: The Czech Academy of Sciences

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1736-1781

Abstract: 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.

Keywords: Large deviations principle; Moderate deviations principle; Primitive equations; Weak convergence approach; 60H15; 60F10; 35Q86 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01125-1

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