An approximation of a Generalized Langevin equations with small mass and randomly fast oscillation is derived. By some bounded estimates and a diffusion approximation the limiting equation is shown to be stochastic partial differential equations (SPDEs) driven by white noise.

中文翻译：

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具有无限个自由度的广义Langevin方程的小质量极限和扩散近似

推导了具有较小质量和随机快速振荡的广义Langevin方程的逼近。通过一些有界估计和扩散近似，极限方程显示为由白噪声驱动的随机偏微分方程（SPDE）。