In this paper, we discuss a class of perturbed second-order stochastic evolution equations. A perturbed second-order stochastic evolution equation for the unperturbed one is proposed. We show the mild solutions of perturbed second-order stochastic evolution equation and the unperturbed one are close on finite time-interval and on interval whose length tends to infinity as small perturbations tend to zero. A class of stochastic partial differential equations with perturbations is proposed as an application to illustrate the theoretical results.

中文翻译：

---

扰动的二阶随机发展方程

在本文中，我们讨论了一类扰动的二阶随机演化方程。提出了一个无扰动的二阶随机随机演化方程。我们显示了扰动的二阶随机演化方程的温和解，无扰动的二阶解在有限的时间间隔和长度上接近，而随着小扰动趋于零，该区间的长度趋于无穷大。提出了一类带有扰动的随机偏微分方程，作为说明理论结果的应用。