In this article, we propose two types of explicit tamed Euler–Maruyama (EM) schemes for neutral stochastic differential delay equations with superlinearly growing drift and diffusion coefficients. The first type is convergent in the ${\mathcal{L}}^q$ sense under the local Lipschitz plus Khasminskii-type conditions. The second type is of order half in the mean-square sense under the Khasminskii-type, global monotonicity and polynomial growth conditions. Moreover, it is proved that the partially tamed EM scheme has the property of mean-square exponential stability. Numerical examples are provided to illustrate the theoretical findings.

中文翻译：

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具有超线性扩散系数的中立随机微分时滞方程的驯服EM格式

在本文中，我们针对漂移和扩散系数超线性增长的中立随机微分延迟方程，提出了两种显式驯服的Euler-Maruyama（EM）方案。第一种类型收敛于${\mathcal{大号}}^q$在当地的Lipschitz加上Khasminskii型条件下的感觉。第二种类型在Khasminskii类型，整体单调性和多项式增长条件下的均方意义上为一半。此外，证明了部分驯服的EM方案具有均方指数稳定性。数值例子说明了理论发现。