In this paper, a modified Euler-Maruyama (EM) method is constructed for a kind of multi-term Riemann-Liouville stochastic fractional differential equations and the strong convergence order min{1-{\alpha}_m, 0.5} of the proposed method is proved with Riemann-Liouville fractional derivatives' orders 0<{\alpha}_1<{\alpha}_2<...<{\alpha}_m <1. Then, based on the sum-of-exponentials approximation, a fast implementation of the modified EM method which is called a fast EM method is derived to greatly improve the computational efficiency. Finally, some numerical examples are carried out to support the theoretical results and show the powerful computational performance of the fast EM method.
翻译：在本文中,为一种多期Riemann-Liouville的随机分差方程式设计了经修改的Euler-Maruyama(EM)方法,而Riemann-Liouville的分衍生物 0 ⁇ alpha1 ⁇ 1 ⁇ alpha ⁇ 2 <... ⁇ alpha ⁇ 2 < 1. 之后,根据特效总和近似值,迅速实施称为快速EM方法的经修改的EM方法,可以极大地提高计算效率。最后,一些数字例子用于支持理论结果,并显示快速EM方法的强大计算性能。
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