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Abstract
In this paper, the truncated Milstein method, that was initially proposed in Guo et al. (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. In addition, the technique of the randomized step-size is employed to raise the convergence rate of the truncated Milstein method. Numerical simulations are provided to illustrate the theoretical results.
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