In this article, we study the McKean-Vlasov neutral stochastic differential delay equations driven by fractional Brownian motion with super-linearly growing coefficients, where the Hurst exponent $H\in(1/2,1)$. The existence and uniqueness of the exact solution were shown by the Picard iteration. Besides, we propose a tamed theta Euler-Maruyama scheme for this equation, analyzed the moment boundness and propagation of chaos etc. Moreover, the convergence rate of the numerical scheme is established.
翻译:本文研究了由分数布朗运动驱动且具有超线性增长系数的McKean-Vlasov中立型随机时滞微分方程,其中赫斯特指数$H\in(1/2,1)$。通过Picard迭代法证明了精确解的存在唯一性。此外,针对该方程提出了驯服theta Euler-Maruyama数值格式,分析了其矩有界性与混沌传播等性质。进一步建立了该数值格式的收敛速率。