In this paper, we consider the asymptotic behaviour of non-autonomous stochastic discrete complex Ginzburg-Landau equations with additive noise in weighted space . The existences of tempered random attractors for this equation in spaces and are proved respectively by tail estimates, which implies that the obtained -random attractor is compact and attracting in the topology of space. The main difficulty here is the lack of compactness on infinite lattices. To deal with this, we introduce a common embedding space of and and derive some tail-estimates of solutions.

中文翻译：

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非自治随机离散复Ginzburg-Landau方程随机吸引子的正则性

在本文中，我们考虑了在加权空间中具有加性噪声的非自治随机离散复数 Ginzburg-Landau 方程的渐近行为。该方程在空间中存在调和随机吸引子，分别通过尾估计证明，这意味着所得到的随机吸引子在空间拓扑结构中是紧致吸引的。这里的主要困难是无限格上缺乏紧凑性。为了解决这个问题，我们引入了 和 的公共嵌入空间，并导出了一些解决方案的尾估计。