We study stochastic model reduction for evolution equations in infinite-dimensional Hilbert spaces and show the convergence to the reduced equations via abstract results of Wong–Zakai type for stochastic equations driven by a scaled Ornstein–Uhlenbeck process. Both weak and strong convergence are investigated, depending on the presence of quadratic interactions between reduced variables and driving noise. Finally, we are able to apply our results to a class of equations used in climate modeling.

中文翻译：

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减少随机模型：收敛性及其在气候方程中的应用

我们研究了无穷维希尔伯特空间中演化方程的随机模型约简，并通过Wong-Zakai类型的抽象结果证明了缩减方程的收敛性，该结果由比例缩放的Ornstein-Uhlenbeck过程驱动。根据减小的变量和行驶噪声之间是否存在二次相互作用，对弱收敛和强收敛进行了研究。最后，我们能够将我们的结果应用于气候模拟中使用的一类方程式。