中文摘要：

本文研究了随机延迟微分方程的平衡方法的收敛性和均方稳定性.利用半鞅收敛定理,给出了真解的渐进稳定和均方稳定的一个更弱的条件.平衡方法下随机延迟微分方程的真解的均方稳定性.

英文摘要：

The paper investigates convergence and mean-square stability of the balancedmethod for stochastic differential delay equation. By applying the semi-martingale convergencetheorem, a weaker condition of asymptotic and mean-square stability of the exact solution is given,the balanced method reproduces mean-square stability of the exact solution for stochastic differen-tial delay equation.