This paper discusses the asymptotic behavior of the solution for a class of perturbed nonlocal stochastic functional differential equations (SFDEs, in short). By comparing it with the solution of the corresponding unperturbed one, we derive the conditions under which their solutions are close. Firstly, the results are established on finite time-intervals. Then, we also show the results hold when the length of time-interval tends to infinity as small perturbations tend to zero.

中文翻译：

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扰动的非局部随机泛函微分方程

本文讨论了一类扰动的非局部随机泛函微分方程（简称SFDE）的解的渐近行为。通过将其与相应的无扰动解进行比较，我们得出了它们的解接近的条件。首先，将结果建立在有限的时间间隔上。然后，当小扰动趋于零时，当时间间隔的长度趋于无穷大时，我们还显示了结果成立。