This paper develops strong convergence of the Euler–Maruyama (EM) schemes for approximating McKean–Vlasov stochastic differential equations (SDEs). In contrast to the existing work, a novel feature is the use of a much weaker condition—local Lipschitzian in the state variable, but under uniform linear growth assumption. To obtain the desired approximation, the paper first establishes the existence and uniqueness of solutions of the original McKean–Vlasov SDE using a Euler-like sequence of interpolations and partition of the sample space. Then, the paper returns to the analysis of the EM scheme for approximating solutions of McKean–Vlasov SDEs. A strong convergence theorem is established. Moreover, the convergence rates under global conditions are obtained.

中文翻译：

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状态变量局部 Lipschitz 条件下 McKean-Vlasov 随机微分方程 Euler-Maruyama 格式的强收敛

本文开发了用于逼近 McKean-Vlasov 随机微分方程 (SDE) 的 Euler-Maruyama (EM) 方案的强收敛性。与现有工作相比，一个新特征是在状态变量中使用更弱的条件——局部 Lipschitzian，但在均匀线性增长假设下。为了获得所需的近似值，本文首先使用类似欧拉的插值序列和样本空间的划分来确定原始 McKean-Vlasov SDE 解的存在性和唯一性。然后，本文回到对 McKean-Vlasov SDE 近似解的 EM 方案的分析。建立了一个强收敛定理。此外，还获得了全局条件下的收敛速度。