In this work, we are concerned with the asymptotic properties of solutions for an impulsive neutral stochastic functional integro-differential equation. By applying the theory of resolvent operators, the Banach fixed point principle theorem, and results on stochastic analysis, we study respectively the existence, uniqueness, and global attracting and quasi-invariant sets of mild solutions for the considered equation. We also derive some sufficient conditions of pth moment exponential stability and almost surely exponential stability of the mild solutions. An example is provided in the end to illustrate the applications of the obtained results.

中文翻译：

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脉冲中立型随机泛函积分微分方程解的渐近性质

在这项工作中，我们关注的是脉冲中立型随机泛函积分微分方程解的渐近性质。通过应用可分解算子理论，Banach不动点原理定理和随机分析结果，我们分别研究了所考虑方程的温和解的存在性，唯一性以及全局吸引和拟不变集。我们还导出了p矩指数稳定性和温和溶液的几乎肯定指数稳定性的一些充分条件。最后提供了一个例子来说明所获得结果的应用。