论文标题
Zakai方程的叠加原理和测量空间上的Fokker-Planck方程
Superposition principles for the Zakai equations and the Fokker-Planck equations on measure spaces
论文作者
论文摘要
这项工作涉及Zakai方程与测量空间上的Fokker-Planck方程之间的叠加。首先，我们证明了$ \ mr^\ mn $在可集成条件下的fokker-planck方程的叠加原则。然后，通过它，我们从非线性滤波问题和fokker-planck方程的弱解决方案中展示了Zakai方程弱解的两个叠加原理。作为副产品，我们提供了一些弱条件，在这些条件下，可以从弱的意义上解决fokker-planck方程。
The work concerns the superposition between the Zakai equations and the Fokker-Planck equations on measure spaces. First, we prove a superposition principle for the Fokker-Planck equations on $\mR^\mN$ under the integrable condition. And then by means of it, we show two superposition principles for the weak solutions of the Zakai equations from the nonlinear filtering problems and the weak solutions of the Fokker-Planck equations on measure spaces. As a by-product, we give some weak conditions under which the Fokker-Planck equations can be solved in the weak sense.
