No abstract

The truncated Milstein method, which was initial proposed in (Guo, Liu, Mao and Yue 2018), is extended to the non-autonomous stochastic differential equations with the super-linear state variable and the Hölder continuous time variable. The convergence rate is proved. Compared with the initial work, the requirements on the step-size is significantly released. In addition, the technique of the randomized step-size is employed to raise the convergence rate of the truncated Milstein method.