Backward Euler method for stochastic differential equations with non-Lipschitz coefficients

05/26/2022

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by   Hao Zhou, et al.

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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.