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

0561775 - ÚTIA 2023 RIV US eng J - Journal Article
Slavík, Jakub
Large and Moderate Deviations Principles and Central Limit Theorem for the Stochastic 3D Primitive Equations with Gradient-Dependent Noise.
Journal of Theoretical Probability. Roč. 35, č. 3 (2022), s. 1736-1781. ISSN 0894-9840. E-ISSN 1572-9230
Institutional support: RVO:67985556
Keywords : large deviations principle * moderate deviations principle * primitive equations * weak convergence approach
OECD category: Statistics and probability
Impact factor: 0.8, year: 2022
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2022/SI/slavik-0561775.pdf https://link.springer.com/article/10.1007/s10959-021-01125-1

We establish the large deviations principle (LDP) and 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 a multiplicative white noise allowing dependence on spatial gradient of solutions with initial data in H2. The LDP is established using the weak convergence approach of Budjihara and Dupuis and uniform version of the stochastic Gronwall lemma. The result corrects a minor technical issue in Z. Dong, J. Zhai, and R. Zhang: Large deviations principles for 3D stochastic primitive equations, J. Differential Equations, 263(5):3110–3146, 2017, and establishes the result for a more general noise. The MDP is established using a similar argument.
Permanent Link: https://hdl.handle.net/11104/0335180