论文标题
完全耦合的McKean-Vlasov SDES的均质速率
Rate of homogenization for fully-coupled McKean-Vlasov SDEs
论文作者
论文摘要
我们考虑了McKean-Vlasov SDE的完全耦合的慢速系统，并完全依赖于缓慢和快速的组件以及缓慢的组件的定律，并将收敛速率推导到其同质化的极限。我们没有做出周期性的假设，而是对快速运动施加条件，以确保过时性。在证据的过程中，我们获得了相关的千古定理，并获得了泊松类型方程的规律性以及具有独立关注的Wasserstein空间上相关的Cauchy-Problem的结果。
We consider a fully-coupled slow-fast system of McKean-Vlasov SDEs 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.
