We study the stochastic 3D primitive equations of the atmospheric mechanics. We consider them under a bounded and non-degenerate noise, which is statistically periodic in time with period 1. In such a case we prove that the associated integer-time Markov chain is exponentially mixing, which means that there exists a unique stationary measure to which the laws of all trajectories of this Markov chain converge exponentially fast.

中文翻译：

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有界非退化噪声下原始方程的混合

我们研究了大气力学的随机3D基本方程。我们认为它们处于有界且非退化的噪声下，该噪声在统计上具有周期1，在时间上是周期性的。在这种情况下，我们证明相关的整数时间马尔可夫链呈指数混合，这意味着存在一个唯一的平稳测度马尔可夫链的所有轨迹定律快速收敛。