Trotter-Kato Approximations of Impulsive Neutral SPDEs in Hilbert Spaces

TL;DR

This paper investigates Trotter-Kato approximations for impulsive neutral stochastic partial differential equations in Hilbert spaces, providing new insights into their solutions and parameter dependence.

Contribution

It introduces the novel combination of Trotter-Kato approximations with impulsive neutral SPDEs, a previously unexplored area.

Findings

Established Trotter-Kato approximation results for these equations

Derived a classical limit theorem on parameter dependence

Extended the theory to impulsive neutral SPDEs in Hilbert spaces

Abstract

This paper studies a class of impulsive neutral stochastic partial differential equations in real Hilbert spaces. The main goal here is to consider the Trotter-Kato approximations of mild solutions of such equations in the $p$th-mean ($p\geq2$). As an application, a classical limit theorem on the dependence of such equations on a parameter is obtained. The novelty of this paper is that the combination of this approximating system and such equations has not been considered before.