论文标题
有缺陷的Fokker-Planck方程中的广义渔民信息
Generalised Fisher Information in Defective Fokker-Planck Equations
论文作者
论文摘要
这项工作的目的是在线性fokker-planck方程中介绍和调查\ textit {广义渔民信息}。该功能取决于两个函数而不是一个功能，表现出与标准Fisher信息相同的衰减行为，并允许我们通过适当的分解研究Fokker-Planck解决方案的不同部分。几乎专注于具有恒定漂移和扩散矩阵的Fokker-Planck方程，我们将使用该新定义的功能对良好的Bakry-Emery方法进行修改，以提供对这种方程相对尖锐的熵行为的替代证明，当时，当散布矩阵积极的确定性和漂移Matrix缺陷时，对此类等式的相对范围的尖锐长期行为。这种新颖的方法与以前的技术不同，并且依赖于Fokker-Planck操作员的最小频谱信息，这与作者以前的作品不同，那里需要来自光谱理论的强大工具。
The goal of this work is to introduce and investigate a \textit{generalised Fisher Information} in the setting of linear Fokker-Planck equations. This functional, which depends on two functions instead of one, exhibits the same decay behaviour as the standard Fisher information, and allows us to investigate different parts of the Fokker-Planck solution via an appropriate decomposition. Focusing almost exclusively on Fokker-Planck equations with constant drift and diffusion matrices, we will use a modification of the well established Bakry-Emery method with this newly defined functional to provide an alternative proof to the sharp long time behaviour of relative entropies of solutions to such equations when the diffusion matrix is positive definite and the drift matrix is defective. This novel approach is different to previous techniques and relies on minimal spectral information on the Fokker-Planck operator, unlike the one presented the authors' previous work, where powerful tools from spectral theory were needed.
