论文标题
希尔伯特空间中随机功能微分方程的不变度量
Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces
论文作者
论文摘要
在这项工作中，我们研究了希尔伯特空间中非线性随机功能分化方程的长期行为。特别是，我们从建立温和解决方案的存在和独特性开始。我们继续在适当的希尔伯特空间中的解决方案的时间范围内得出小修道院的统一。这些界限使我们能够基于Krylov-Bogoliubov定理建立不变措施的存在，以实现措施家族的紧密度。最后，在某些关于非线性的假设下，我们确定了不变措施的独特性。
In this work we study the long time behavior of nonlinear stochastic functional-differential equations in Hilbert spaces. In particular, we start with establishing the existence and uniqueness of mild solutions. We proceed with deriving a priory uniform in time bounds for the solutions in the appropriate Hilbert spaces. These bounds enable us to establish the existence of invariant measure based on Krylov-Bogoliubov theorem on the tightness of the family of measures. Finally, under certain assumptions on nonlinearities, we establish the uniqueness of invariant measures.
