Periodic averaging theorems for neutral stochastic functional differential equations involving delayed impulses

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.