We study the traditional backward Euler method for $m$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H > 1/2$ whose drift coefficient satisfies the one-sided Lipschitz condition. The backward Euler scheme is proved to be of order $1$ and this rate is optimal by showing the asymptotic error distribution result. Two numerical experiments are performed to validate our claims about the optimality of the rate of convergence.

翻译：我们研究的是传统的落后Euler方法,该方法由分数布朗运动驱动的以赫斯特参数($H > 1/2美元,其漂移系数符合单向利普施茨条件)驱动的低度Euler 法,落后Euler 法被证明符合1美元标准,通过显示无症状误差分布结果,这一比率是最佳的。我们进行了两个数字实验,以证实我们关于趋同率最佳性的说法。