论文标题
Lipschitz的规律性不变的随机动力学系统量度
Lipschitz regularity of the invariant measure of random dynamical systems
论文作者
论文摘要
在本文中，我们得出了与一类随机动力学系统-RDS相关的不变度度量分解的规律性结果。这项工作的结果是通过构建由Wasserstein-Kantorovich样公制定义的合适各向异性规范空间获得的，并了解其固定点附近相关转移操作员的动力学。确切地说，我们采用功能分析技术来证明其在适当的签名度量空间上的作用的光谱差距。我们应用此分析来证明Lipschitz可观察到RDS的相关语句的指数衰减。
In this article we derive a regularity result for the disintegration of the invariant measure associated to a class of Random Dynamical Systems - RDS. The results of this work are obtained by constructing a suitable anisotropic normed space defined by the Wasserstein-Kantorovich-like metric and understanding the dynamics of the associated transfer operator in a neighborhood of its fixed point. Precisely, we employ functional analytic techniques to demonstrate a spectral gap for its action on suitable spaces of signed measures. We apply this analysis to prove an exponential decay of correlation statement for Lipschitz observables and statistical properties of the RDS.
