In this paper we study a type of stochastic McKean-Vlasov equations with non-Lipschitz coefficients. Firstly, by an Euler-Maruyama approximation existence of its weak solutions is proved. And then we observe pathwise uniqueness of its weak solutions. Finally, it is shown that the Euler-Maruyama approximation has an optimal strong convergence rate.

中文翻译：

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具有非 Lipschitz 系数的随机 McKean-Vlasov 方程的 Euler-Maruyama 近似

在本文中，我们研究了一类具有非 Lipschitz 系数的随机 McKean-Vlasov 方程。首先，通过Euler-Maruyama近似证明了其弱解的存在性。然后我们观察其弱解的路径唯一性。最后，证明了 Euler-Maruyama 近似具有最优的强收敛速度。