A new explicit Milstein-type scheme for SDE driven by Lévy noise is proposed where both drift and diffusion coefficients are allowed to grow super-linearly. The strong rate of convergence (in $ \mathcal{L}^2 $-sense) is shown to be arbitrarily close to one which is consistent with the corresponding result on the classical Milstein scheme obtained for coefficients satisfying global Lipschitz conditions.

中文翻译：

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具有超线性系数的Lévy噪声驱动的SDE的Milstein型方案

提出了一种新的由Lévy噪声驱动的SDE的显式Milstein型方案，其中漂移系数和扩散系数都允许超线性增长。强大的收敛速度（以$ \ mathcal {L} ^ 2 $ -sense）被证明是任意接近的，这与经典Milstein方案针对满足全局Lipschitz条件的系数所获得的相应结果是一致的。