Backward Euler method for stochastic differential equations with non-Lipschitz coefficients driven by fractional Brownian motion.

We study the traditional backward Euler method for stochastic differential equation driven by fractional Brownian motion whose drift coefficient satisfies the one-sided Lipschitz condition. The backward Euler scheme is proved to be of order one and this rate is optimal by showing the asymptotic error distribution result. Numerical experiments are performed to validate our claims about the optimality of the rate of convergence. [ABSTRACT FROM AUTHOR]