Tamed Euler–Maruyama approximation of McKean–Vlasov stochastic differential equations with super-linear drift and Hölder diffusion coefficients

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This paper establishes the strong convergence of the tamed Euler–Maruyama (EM) approximation for McKean–Vlasov stochastic differential equations (SDEs) with super-linear drift and Hölder diffusion coefficients. By the Yamada-Watanable technique, this paper deals with the Hölder diffusion coefficient. To obtain the desired approximation, this paper also proves the existence and uniqueness of strong solution for this class of McKean-Vlasov SDEs. When one-sided local Lipschitz condition is replaced by the global condition, the convergence rate can be obtained. Finally, two examples are presented to illustrate our results.