This paper is concerned with the numerical approximations for stochastic differential equations with non-Lipschitz drift or diffusion coefficients. A modified truncated Euler-Maruyama discretization scheme is developed. Moreover, by establishing the criteria on stochastic C-stability and B-consistency of the truncated Euler-Maruyama method, we obtain the strong convergence and the convergence rate of the numerical method. Finally, numerical examples are given to illustrate our theoretical results.

中文翻译：

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非Lipschitz随机微分方程截断Euler-Maruyama方法的改进

本文关注具有非 Lipschitz 漂移或扩散系数的随机微分方程的数值近似。开发了一种改进的截断 Euler-Maruyama 离散化方案。此外，通过建立截断Euler-Maruyama方法的随机C稳定性和B一致性准则，获得了数值方法的强收敛性和收敛速度。最后，给出数值例子来说明我们的理论结果。