In this paper, we continue investigating the strong convergence order of the Euler method for Volterra integro-differential equations with fractional Brownian motions. The strong convergence order for a long-memory process is improved by the method with distributions of the centered Gaussian processes. Moreover, for a short-memory process, the optimal strong convergence order of the method with distributions under uniform and graded meshes is discussed. Numerical examples illustrate our theoretical results.

中文翻译：

---

具有分数布朗运动的Volterra积分-微分方程的强收敛性分析

在本文中，我们继续研究分数阶布朗运动的Volterra积分微分方程的Euler方法的强收敛阶。通过集中高斯过程的分布方法，可以改善长存储过程的强收敛阶。此外，对于短存储过程，讨论了在均匀且渐变网格下具有分布的方法的最佳强收敛阶。数值例子说明了我们的理论结果。