In this paper, we are concerned with the convergence rate of Euler–Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) of neutral type, where the neutral, drift, and diffusion terms are allowed to be of polynomial growth. More precisely, for SDDEs of neutral type driven by Brownian motions, we reveal that the convergence rate of the corresponding EM scheme is one-half; Whereas for SDDEs of neutral type driven by pure jump processes, we show that the best convergence rate of the associated EM scheme is slower than one-half. As a result, the convergence rate of general SDDEs of neutral type, which is dominated by pure jump process, is slower than one-half.

中文翻译：

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中性型SDDE的Euler-Maruyama方案的收敛速度

在本文中，我们关注中立型随机微分延迟方程（SDDE）的Euler–Maruyama（EM）方案的收敛速度，其中中立项，漂移项和扩散项允许多项式增长。更准确地说，对于由布朗运动驱动的中性类型的SDDE，我们发现相应的EM方案的收敛速度是二分之一。而对于由纯跳跃过程驱动的中性类型的SDDE，我们证明了相关EM方案的最佳收敛速度比一半慢。结果，以纯跳跃过程为主的中性类型的一般SDDE的收敛速度比一半慢。