Mean square exponential stability of $\theta$-EM and modified truncated Euler-Maruyama (MTEM) methods for stochastic differential delay equations (SDDEs) are investigated in this paper. We present new criterion of mean square exponential stability of the $\theta$-EM and MTEM methods for SDDEs, which are different from most existing results under Khasminskii-type conditions. Two examples are provided to support our conclusions.

翻译：本文研究了随机延迟微分方程(SDDEs)的$\theta$-EM方法和修正截断Euler-Maruyama(MTEM)方法的均方指数稳定性。我们给出了SDDEs的$\theta$-EM和MTEM方法均方指数稳定性的新判据，该判据不同于Khasminskii型条件下的大多数现有结果。文中提供了两个算例以验证所得结论。