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arXiv · 2011.00023

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

Juan Liao·Wei Liu·Xiaoyan Wang
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Abstract

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 H\"older 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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Juan Liao, Wei Liu, Xiaoyan Wang. 2020-10-30. Truncated Milstein method for non-autonomous stochastic differential equations and its modification. https://arxiv.org/abs/2011.00023

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