In this paper, we present homogenization and corrector results for stochastic linear parabolic equations in periodically perforated domains with non-homogeneous Robin conditions on the holes. We use the periodic unfolding method and probabilistic compactness results. Homogenization results presented in this paper are stochastic counterparts of some fundamental work given in [Cioranescu, Donato and Zaki in Port. Math. (N.S.) 63 (2006), 467–496]. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized problem, which is a parabolic stochastic equation in fixed domain with Dirichlet condition on the boundary. In contrast to the two scale convergence method, the corrector results obtained in this paper are without any additional regularity assumptions on the solutions of the original problems.

中文翻译：

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周期性穿孔区域线性随机方程Robin问题的同质化和校正。

在本文中，我们给出了在孔上具有非均匀Robin条件的周期穿孔区域中的随机线性抛物方程的均化和校正结果。我们使用周期性展开方法和概率紧致性结果。本文介绍的均质化结果与[Cioranescu，Donato和Zaki在港口的一些基本工作是随机对应的。数学。（NS）63（2006），467–496]。我们表明，原始问题的解决方案序列在合适的拓扑结构中收敛到均匀化问题的解决方案，该问题是边界上具有Dirichlet条件的固定域中的抛物型随机方程。与两种规模收敛方法相反，