论文标题
确定性动力学系统的不变性原理中的Wasserstein收敛速率
Wasserstein convergence rates in the invariance principle for deterministic dynamical systems
论文作者
论文摘要
在本文中，我们考虑了确定性非均匀双曲系统的不变性原理中的瓦斯汀距离的收敛速率，其中包括离散的时间系统和流。我们的结果适用于统一的双曲系统和大量的非均匀双曲系统，包括间歇地图，Viana地图，有限的地平线平面周期性Lorentz气体等。此外，作为对同质化问题的非平凡应用，我们研究了$ \ MATHCAL {W} _2 $ -Convergence速率的快速离散确定性系统到随机微分方程。
In this paper, we consider the convergence rate with respect to Wasserstein distance in the invariance principle for deterministic nonuniformly hyperbolic systems, where both discrete time systems and flows are included. Our results apply to uniformly hyperbolic systems and large classes of nonuniformly hyperbolic systems including intermittent maps, Viana maps, finite horizon planar periodic Lorentz gases and others. Furthermore, as a nontrivial application to homogenization problem, we investigate the $\mathcal{W}_2$-convergence rate of a fast-slow discrete deterministic system to a stochastic differential equation.
