论文标题
大型海洋循环的三维行星地球方程的大偏差原理具有小乘噪声
Large deviation principle for the three dimensional planetary geostrophic equations of large-scale ocean circulation with small multiplicative noise
论文作者
论文摘要
我们证明了大规模海洋循环的三维随机行星地球循环方程的小噪声极限中的较大偏差原理。在本文中，我们首先通过单调性的方法证明了该系统薄弱解决方案的适应性。众所周知，最近开发的方法是一种弱收敛方法，用于研究较大的偏差，该方法基本上基于\ cite {Ba2}的主要结果，该结果揭示了指数积分相对于布朗噪声的变异表示。 ITô不平等和Burkholder-Davis-Gundy不平等是我们证明的主要工具，而Budhiraja，Dupuis和Ganguly在\ cite {Ba3}中提出的弱收敛方法也用于建立大偏差原则。
We demonstrate the large deviation principle in the small noise limit for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation. In this paper, we first prove the well-posedness of weak solutions to this system by the method of monotonicity. As we know, a recently developed method, weak convergent method, has been employed in studying the large deviations and this method is essentially based on the main result of \cite{ba2} which discloses the variational representation of exponential integrals with respect to the Brownian noise. The Itô inequality and Burkholder-Davis-Gundy inequality are the main tools in our proofs, and the weak convergence method introduced by Budhiraja, Dupuis and Ganguly in \cite{ba3} is also used to establish the large deviation principle.
