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Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion
Annales Henri Poincaré ( IF 1.5 ) Pub Date : 2020-02-08 , DOI: 10.1007/s00023-020-00889-2
Soon Hoe Lim , Jan Wehr , Maciej Lewenstein

We study homogenization for a class of generalized Langevin equations (GLEs) with state-dependent coefficients and exhibiting multiple time scales. In addition to the small mass limit, we focus on homogenization limits, which involve taking to zero the inertial time scale and, possibly, some of the memory time scales and noise correlation time scales. The latter are meaningful limits for a class of GLEs modeling anomalous diffusion. We find that, in general, the limiting stochastic differential equations for the slow degrees of freedom contain non-trivial drift correction terms and are driven by non-Markov noise processes. These results follow from a general homogenization theorem stated and proven here. We illustrate them using stochastic models of particle diffusion.

中文翻译:

广义Langevin方程的同质化及其在异常扩散中的应用。

我们研究一类具有状态相关系数并表现出多个时间尺度的广义Langevin方程(GLE)的均质化。除了较小的质量限制外,我们还将重点放在均化限制上,这涉及将惯性时间标度以及可能的一些存储时间标度和噪声相关时间标度设为零。后者对于建模异常扩散的GLE类是有意义的限制。我们发现,一般来说,慢自由度的极限随机微分方程包含非平凡的漂移校正项,并且受非马尔可夫噪声过程的驱动。这些结果来自此处陈述和证明的一般均化定理。我们使用粒子扩散的随机模型来说明它们。
更新日期:2020-02-08
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