论文标题
大偏差原理通过Malliavin微积分，用于由退化白色噪声驱动的Navier-Stokes系统
Large deviations principle via Malliavin calculus for the Navier-Stokes system driven by a degenerate white-in-time noise
论文作者
论文摘要
本文的目的是为二维随机Navier-Stokes系统建立Donsker-Varadhan型大偏差原理（LDP）。主要的新颖性是，假定噪声在傅立叶空间中高度退化。该证明是通过使用Arxiv：1410.6188在离散时间设置中开发的LDP的标准进行的，并在Arxiv中扩展：1505.03686至连续时间。该标准的主要条件之一是Feynman-Kac Semigroup的统一伐木属性，我们通过使用Malliavin conculus来验证。
The purpose of this paper is to establish the Donsker-Varadhan type large deviations principle (LDP) for the two-dimensional stochastic Navier-Stokes system. The main novelty is that the noise is assumed to be highly degenerate in the Fourier space. The proof is carried out by using a criterion for the LDP developed in arXiv:1410.6188 in a discrete-time setting and extended in arXiv:1505.03686 to the continuous-time. One of the main conditions of that criterion is the uniform Feller property for the Feynman-Kac semigroup, which we verify by using Malliavin calculus.
