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arXiv 2011.000232020-11math.NAcs.NAmath.PR

Truncated Milstein method for non-autonomous stochastic differential equations and its modification

Juan Liao, Wei Liu, Xiaoyan Wang

备注：: 25 pages, 2 figures

英文摘要：

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.

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