Large and moderate deviations principles and central limit theorem for\n the stochastic 3D primitive equations with gradient dependent noise

2020/10/24 by Jakub Slavík, Slavík, Jakub · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #35Q86 #60F10 #60H15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2010.12843

openalex publication_date 2020/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the large deviations principle (LDP) and the moderate deviations\nprinciple (MDP) and an almost sure version of the central limit theorem (CLT)\nfor the stochastic 3D viscous primitive equations driven by a multiplicative\nwhite noise allowing dependence on spatial gradient of solutions with initial\ndata in H². The LDP is established using the weak convergence approach of\nBudjihara and Dupuis and uniform version of the stochastic Gronwall lemma. The\nresult corrects a minor technical issue in Z. Dong, J. Zhai, and R. Zhang:\nLarge deviations principles for 3D stochastic primitive equations, J.\nDifferential Equations, 263(5):3110-3146, 2017, and establishes the result for\na more general noise. The MDP is established using a similar argument.\n

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• The large deviation principle for the stochastic 3D primitive equations with transport noise

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