In this paper, we consider a fully-coupled slow–fast system of McKean–Vlasov stochastic differential equations with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy problem on the Wasserstein space that are of independent interest.

中文翻译：

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全耦合 McKean–Vlasov SDE 的均化率

在本文中，我们考虑了完全依赖于慢分量和快分量以及慢分量定律的 McKean-Vlasov 随机微分方程的完全耦合慢-快系统，并导出收敛速度到其均匀化极限。我们不做周期性假设，但我们对快速运动施加条件以保证遍历性。在证明过程中，我们获得了相关的遍历定理，并获得了关于泊松型方程的正则性以及 Wasserstein 空间上相关的 Cauchy 问题的结果，这些结果是独立的。