This paper focuses on the numerical scheme for delay-type stochastic McKean-Vlasov equations (DSMVEs) driven by fractional Brownian motion with Hurst parameter $H\in (0,1/2)\cup (1/2,1)$. The existence and uniqueness of the solutions to such DSMVEs whose drift coefficients contain polynomial delay terms are proved by exploting the Banach fixed point theorem. Then the propagation of chaos between interacting particle system and non-interacting system in $\mathcal{L}^p$ sense is shown. We find that even if the delay term satisfies the polynomial growth condition, the unmodified classical Euler-Maruyama scheme still can approximate the corresponding interacting particle system without the particle corruption. The convergence rates are revealed for $H\in (0,1/2)\cup (1/2,1)$. Finally, as an example that closely fits the original equation, a stochastic opinion dynamics model with both extrinsic memory and intrinsic memory is simulated to illustrate the plausibility of the theoretical result.

翻译：本文研究由Hurst参数$H\in (0,1/2)\cup (1/2,1)$的分数布朗运动驱动的时滞型随机McKean-Vlasov方程（DSMVE）的数值格式。通过运用Banach不动点定理，证明了漂移系数含多项式时滞项的此类DSMVE解的存在唯一性。随后在$\mathcal{L}^p$意义下展示了相互作用粒子系统与非相互作用系统之间的混沌传播性质。研究发现，即使时滞项满足多项式增长条件，未经修正的经典Euler-Maruyama格式仍能无粒子退化地逼近相应的相互作用粒子系统。文中揭示了$H\in (0,1/2)\cup (1/2,1)$情形下的收敛速率。最后，作为紧密契合原方程的实际案例，对同时包含外源性记忆与内源性记忆的随机观点动力学模型进行了数值模拟，以验证理论结果的合理性。