中立型变时滞随机微分方程数值解的强收敛性

Strong convergence of numerical solutions of neutral stochastic differential equations with time-dependent delay

讨论中立型变时滞随机微分方程改进的修正截断Euler-Maruyama(EM)方法的q阶矩强收敛性,并得到收敛速度。结果表明此方法适用于高度非线性的漂移项和扩散项,且相较于隐式的修正截断EM方法计算量更小,适用范围更广。

Strong convergence of the modified truncated Euler-Maruyama method for stochastic differential equa-tions with a time-dependent delay is discussed,and the convergence rate is obtained.This method can be applied to neutral stochastic differential delay equations(NSDDEs)with highly nonlinear drift and diffusion terms.Com-pared with the implicit modified truncated Euler-Maruyama method,the amount of calculation required is reduced and the application range is wider.