This paper aims at addressing the issue of a periodic averaging method for neutral stochastic functional differential equations with delayed impulses. Two periodic averaging theorems are presented and the approximate equivalence between the solutions to the original systems and those to the reduced averaged systems without impulses is proved. Further, we show a brief framework of extending our main results to Lévy case. At last, an example is given to demonstrate the procedure and validity of the proposed periodic averaging method.

中文翻译：

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涉及延迟脉冲的中性随机泛函微分方程的周期平均定理

本文旨在解决具有延迟脉冲的中性随机泛函微分方程的周期平均方法问题。提出了两个周期平均定理，并证明了原始系统的解与没有脉冲的简化平均系统的解之间的近似等价性。此外，我们展示了将主要结果扩展到 Lévy 案例的简要框架。最后，给出一个例子来证明所提出的周期平均方法的过程和有效性。