一类随机微分方程欧拉格式的收敛性

为进一步研究标量自治随机微分方程的数值解,给出了求解方程的欧拉格式,证明了方程的偏移系数和扩散系数均满足全局Lipschitz条件时的收敛性,并求出了局部收敛阶和均方强收敛阶.证明过程中放宽了限制条件,也得到了与系数满足全局Lipschitz条件和线性增长条件时相同的收敛阶.

Convergence of the Euler scheme for a class of stochastic differential equations

The Euler scheme for the scalar autonomous stochastic differential equations is presented in order to research the numerical solution of the equations.It is proved that the equations are convergent when the deviation coefficient and diffusion coefficient satisfy the global Lipschitz condition.The local convergence order and the mean square strong convergence order are presented as well.The solution process is carried out under relaxed definite conditions,but it also has the same convergence order when the coefficients of the equations satisfy the global Lipschitz condition and the linear growth condition.