Following the ideas of Zhikov and Piatnitski (Izv Math 70(1):19–67, 2006), and more precisely the stochastic two-scale convergence, this paper establishes a homogenization theorem in a stochastic setting for two nonlinear equations: the equation of harmonic maps into the sphere and the Landau–Lifschitz–Gilbert equation. These equations have strong nonlinear features, and in general their solutions are not unique.

中文翻译：

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Landau–Lifshitz–Gilbert方程的随机均质化

遵循Zhikov和Piatnitski（Izv Math 70（1）：19-67，2006）的思想，更确切地说是随机的两尺度收敛，本文建立了一个随机设置的均化定理，用于两个非线性方程：谐波映射到球体和Landau–Lifschitz–Gilbert方程。这些方程具有很强的非线性特征，通常它们的解不是唯一的。