论文标题
SDE的熵的规律性和指数性磨性，由分布依赖噪声驱动
Regularities and Exponential Ergodicity in Entropy for SDEs Driven by Distribution Dependent Noise
论文作者
论文摘要
作为表征随机系统规律性特性的两个关键工具，已对日志不平等和BISMUT公式进行了深入研究，以进行分配依赖性（McKean-Vlasov）SDES。但是，由于技术困难，现有的结果主要集中在没有分配噪声的情况下。在本文中，我们介绍了一个噪声分解论点，以建立对数 - 哈纳克的不平等和bismut公式 在非分类和退化情况下，具有分布依赖性噪声的SDE。作为应用，研究了熵中的指数式磨牙。
As two crucial tools characterizing regularity properties of stochastic systems, the log-Harnack inequality and Bismut formula have been intensively studied for distribution dependent (McKean-Vlasov) SDEs. However, due to technical difficulties, existing results mainly focus on the case with distribution free noise. In this paper, we introduce a noise decomposition argument to establish the log-Harnack inequality and Bismut formula for SDEs with distribution dependent noise, in both non-degenerate and degenerate situations. As application, the exponential ergodicity in entropy is investigated.
