求解随机微分方程的欧拉法的收敛性

Convergence of the Euler scheme for stochastic differential equation

对于求解随机微分方程的数值方法 ,给出了衡量其有效性的标准之一即强收敛性 .证明了欧拉法用于求解标量自治随机微分方程时 ,在方程的偏移系数和扩散系数均满足线性增长条件和全局李普希兹条件的情形下 ,当噪声为增加噪声和附加噪声时 ,欧拉法的收敛阶分别为 0 .5和 1 .0 .

In designing numerical schemes for solving stochastic differential equations, the definition of strong convergence was given. It was one of the criteria to measure the efficiency of a numerical scheme. When Euler scheme was used to solve the scalar autonomous stochastic differential equations and both of the drift coefficient and diffusion coefficient satisfied the linear growth condition and global Lipschitz condition, it was shown that the convergence order of Euler was 0.5 and 1.