This paper focuses on systems of stochastic partial differential equations with impulse effects. We establish an averaging principle such that the solution to the complex original nonlinear impulsive stochastic evolution equations can be approximated by that to the more simplified averaged stochastic evolution equations without impulses. By adopting stochastic analysis theory, semigroup approach and inequality technique, sufficient conditions are formulated and the mean square convergence is proved. This ensures that we can concentrate on the averaged system instead of the original system, thus providing a solution for reduction of complexity.

中文翻译：

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脉冲随机偏微分方程的平均原理

本文重点研究具有脉冲效应的随机偏微分方程组。我们建立了一个平均原理，使得复杂的原始非线性脉冲随机演化方程的解可以近似为更简化的无脉冲平均随机演化方程的解。采用随机分析理论、半群法和不等式技术，建立了充分条件，证明了均方收敛性。这确保我们可以专注于平均系统而不是原始系统，从而提供降低复杂性的解决方案。