研究了具有一般衰减率的脉冲随机泛函微分方程的$p$阶矩稳定性问题. 利用Lyapunov泛函法、随机分析理论和文章所建立的脉冲微分不等式, 得到了该方程在一般衰减率下$p$阶矩稳定性和几乎必然稳定性的一些充分性条件. 所得的这些条件既简单又具有一般性, 并被应用于讨论了一般衰减率下脉冲随机时滞微分方程的$p$阶矩稳定性问题. 实例表明,所得结果是有效的和实用的.

This paper investigates the $p$-moment stability with general decay rate of impulsive stochastic functional differential equations. Based on Lyapunov functional method, stochastic analysis theory and the impulsive differential inequality established in this paper, some sufficient conditions on $p$-moment stability and almost sure stability with general decay rate are derived. The obtained results are more general and simple, and are used to deal with impulsive stochastic delay differential equations. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.