In this paper, a stochastic neutral partial functional differential equation is studied in real separable Hilbert spaces. The aim here is to introduce Trotter-Kato approximations of mild solutions for this class of equations. As an application, a classical limit theorem on the dependence of such equations on a parameter is obtained. Moreover, weak convergence of probability measures induced by the Trotter-Kato approximate mild solutions is established. An example is included at the end.

中文翻译：

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随机中性偏泛函微分方程的 Trotter-Kato 近似

本文研究了实可分希尔伯特空间中的随机中性偏泛函微分方程。这里的目的是介绍这类方程的温和解的 Trotter-Kato 近似。作为应用，获得了关于此类方程对参数的依赖性的经典极限定理。此外，建立了由 Trotter-Kato 近似温和解引起的概率测度的弱收敛性。最后附上一个例子。