论文标题
依赖空间分布的Zakai方程的独特性和叠加
Uniqueness and superposition of the space-distribution dependent Zakai equations
论文作者
论文摘要
这项工作涉及来自麦基恩 - 维拉索夫随机微分方程的非线性过滤问题的Zakai方程，并带有相关的噪声。首先，我们建立了依赖空间分布的库什纳 - 斯特拉托尼维奇方程和依赖于空间分布的zakai方程。然后，显示了其强解决方案的路径唯一性。最后，我们证明了依赖于空间分布的Zakai方程和依赖空间分布的Fokker-Planck方程之间的叠加原理。作为副产品，我们提供了一些条件，在这些条件下，依赖于空间分布的fokker-planck方程的解决方案较弱。
The work concerns the space-distribution dependent Zakai equations from nonlinear filtering problems of McKean-Vlasov stochastic differential equations with correlated noises. First of all, we establish the space-distribution dependent Kushner-Stratonovich equations and the space-distribution dependent Zakai equations. Then, the pathwise uniqueness of their strong solutions is shown. Finally, we prove a superposition principle between the space-distribution dependent Zakai equations and space-distribution dependent Fokker-Planck equations. As a by-product, we give some conditions under which space-distribution dependent Fokker-Planck equations have weak solutions.
