Recently, Hong et al. (2020) established the strong convergence rate of the backward Euler scheme for the Cox–Ingersoll–Ross (CIR) model driven by fractional Brownian motion with Hurst parameter $H\in (1/2,1)$, which may effect the efficiency of computation. Taking advantage of being explicit and easily implementable, a positivity preserving explicit scheme is proposed in this paper. For overcoming the difficulties caused by the unbounded diffusion coefficient, an auxiliary equation with a constant diffusion coefficient obtained by proper Lamperti transformation is used. By means of Malliavin calculus, we show that the truncated Euler–Maruyama scheme applied to this auxiliary equation not only ensures the positivity of the numerical solution, but also has the $H$-order rate of the root mean square error over a finite time interval. Furthermore, by transforming back, an explicit scheme for the original CIR model is obtained and has the same convergence order. Finally, some numerical experiments are provided to illustrate the theoretical results.

最近，洪等人。（2020）为具有赫斯特参数的分数布朗运动驱动的 Cox-Ingersoll-Ross (CIR) 模型建立了反向欧拉方案的强收敛速度$H\in (1/2,1)$，这可能会影响计算的效率。利用显式和易于实现的优点，本文提出了一种保持正性的显式方案。为了克服无界扩散系数带来的困难，使用了通过适当的Lamperti变换获得的具有恒定扩散系数的辅助方程。通过 Malliavin 演算，我们证明了应用于该辅助方程的截断 Euler-Maruyama 格式不仅保证了数值解的正性，而且具有$H$- 有限时间间隔内均方根误差的阶率。此外，通过反变换，获得了原始 CIR 模型的显式方案，并且具有相同的收敛阶。最后，提供了一些数值实验来说明理论结果。