2020/10/30 by Liao, Juan, Liu, Wei, Wang, Xiaoyan
#FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)
paper · doi:10.48550/arxiv.2011.00023
The truncated Milstein method, which was initially 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 also significantly released. In addition, the technique of the randomized step-size is employed to raise the convergence rate of the truncated Milstein method.