In this paper, we study the Wong–Zakai approximations of a class of second-order stochastic lattice systems with additive noise. We first prove the existence of tempered pullback attractors for lattice systems driven by an approximation of the white noise. Then, we establish the upper semicontinuity of random attractors for the approximate system as the size of approximation approaches zero.

中文翻译：

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由加性白噪声驱动的二阶随机晶格系统的 Wong-Zakai 近似

在本文中，我们研究了一类具有加性噪声的二阶随机晶格系统的 Wong-Zakai 近似。我们首先证明了由白噪声近似驱动的晶格系统的回火吸引子的存在。然后，我们为近似系统建立随机吸引子的上半连续性，因为近似的大小接近于零。