论文标题
随机3D原始方程的较大和中等偏差原理和中心极限定理具有梯度依赖性噪声
Large and moderate deviations principles and central limit theorem for the stochastic 3D primitive equations with gradient dependent noise
论文作者
论文摘要
我们建立了较大的偏差原理（LDP）和中等偏差原理（MDP），并为随机3D粘性粘性原始方程的中心极限定理（CLT）的几乎确定版本，该方程式由乘以$ h^2 $的最初数据的乘数梯度的多种白噪声驱动。使用Budjihara和Dupuis的弱收敛方法以及随机Gronwall引理的均匀版本建立了LDP。该结果纠正了Z. dong，J。Zhai和R. Zhang的次要技术问题：3D随机原始方程的大偏差原理，J。微分方程，263（5）：3110-3146，2017，并确定了更一般噪声的结果。 MDP是使用类似参数建立的。
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 $H^2$. 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.
