We study the Euler scheme for scalar non-autonomous stochastic differential equations, whose diffusion coefficient is not globally Lipschitz but a fractional power of a globally Lipschitz function. We analyse the strong error and establish a criterion, which relates the convergence order of the Euler scheme to an inverse moment condition for the diffusion coefficient. Our result in particular applies to Cox-Ingersoll-Ross-, Chan-Karolyi-Longstaff-Sanders- or Wright-Fisher-type stochastic differential equations and thus provides a unifying framework.

翻译：我们研究标量非自治随机微分方程的欧拉格式，其扩散系数并非全局Lipschitz，而是某个全局Lipschitz函数的分数次幂。我们分析了强误差，并建立了一个准则，该准则将欧拉格式的收敛阶与扩散系数的逆矩条件相联系。该结果尤其适用于Cox-Ingersoll-Ross型、Chan-Karolyi-Longstaff-Sanders型或Wright-Fisher型随机微分方程，从而提供了一个统一的框架。