论文标题
具有非lipschitz系数的随机微分方程的向后欧拉方法
Backward Euler method for stochastic differential equations with non-Lipschitz coefficients
论文作者
论文摘要
我们研究了传统的向后欧拉方法，用于$ m $ $二维的随机微分方程，该方程是由布朗尼运动的分数运动驱动的，其漂移系数满足单方面的Lipschitz条件。向后的Euler方案被证明是$ 1 $，通过显示渐近误差分布结果，此速率是最佳的。进行了两个数值实验，以验证我们对收敛速率最佳性的主张。
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.
