论文标题
多尺度随机系统的平均原理和正常偏差
Averaging principle and normal deviations for multiscale stochastic systems
论文作者
论文摘要
我们研究具有非平滑系数的不均匀多尺度随机动力学系统的渐近行为。根据平均制度和均质化制度，建立了大型类型功能定律的平均原理中的两种强大融合。然后，我们考虑系统围绕其平均值的小波动。获得了9例功能性中心极限类型定理。特别是，即使原始系统的平均方程式相同，由于快速尺度和偏差尺度之间的相互作用差异，正常偏差的相应均质化极限也可能完全不同。我们为每种情况提供非常直观的解释。此外，获得了强收敛和功能性中心极限定理的尖锐速率，并且这些融合仅依赖于系统系数相对于慢速变量的规律性，并且不依赖于它们在快速变量方面的规律性，这与限制方程相一致，因为在限制方程中完全构成了快速组成的范围，或者完全是远离的。
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle of functional law of large numbers type are established. Then we consider the small fluctuations of the system around its average. Nine cases of functional central limit type theorems are obtained. In particular, even though the averaged equation for the original system is the same, the corresponding homogenization limit for the normal deviation can be quite different due to the difference in the interactions between the fast scales and the deviation scales. We provide quite intuitive explanations for each case. Furthermore, sharp rates both for the strong convergences and the functional central limit theorems are obtained, and these convergences are shown to rely only on the regularity of the coefficients of the system with respect to the slow variable, and do not depend on their regularity with respect to the fast variable, which coincide with the intuition since in the limit equations the fast component has been totally averaged or homogenized out.
