FULL IMPLICIT EULER METHOD FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS
随机延迟微分方程的全隐式Euler方法

It is very important to study the numerical solution of the stochastic delay differential equation, now there exist the explicit and the semi-implicit numerical methods and does't exist the full implicit numerical methods. In this paper, a class of the full implicit Euler method is given. In the full implicit schemes increments of Wiener processes are substituted by some truncated random variables, then, we prove that the method converges with the order 1/2 and the property of convergence of the methods is verified by the numerical experiments. Finally, the numerical experiments show the property of stability of the full implicit methods is better than that of the semi-implicit methods under some situation.