We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order $1/4$ in $L_1$ and $L_2$ for the parameter regime $\kappa\theta>\sigma^2$. We then extend the new method to cover all parameter values by introducing a \emph{soft zero} region (where the deterministic flow determines the approximation) giving a hybrid type method to deal with the reflecting boundary. From numerical simulations we observe a rate of order $1$ when $\kappa\theta>\sigma^2$ rather than $1/4$. Asymptotically, for large noise, we observe that the rates of convergence decrease similarly to those of other schemes but that the proposed method making use of adaptive timestepping displays smaller error constants.

翻译：我们提出一种用于Cox-Ingersoll-Ross模型强数值解的新分裂方法。该方法应用于确定性网格和自适应随机网格时，我们在参数区域$\kappa\theta>\sigma^2$下证明了$L_1$和$L_2$范数中阶数为$1/4$的一致矩界和强误差结果。随后，通过引入一个"软零"区域（其中确定性流决定近似值），我们将新方法推广到覆盖所有参数值，从而得到一种处理反射边界的混合型方法。数值模拟表明，当$\kappa\theta>\sigma^2$时观察到的速率阶数为$1$而非$1/4$。对于大噪声情况，渐近分析显示收敛速率与其他方案类似地下降，但所提出的采用自适应时间步进的方法显示出更小的误差常数。