论文标题
McKean-Vlasov SDE的混乱传播的强烈融合与单数相互作用
Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions
论文作者
论文摘要
在这项工作中，我们显示了混乱的繁殖强烈的融合，用于具有单数$ l^p $互动的麦基vlasov sdes粒子近似以及在粒子轨迹水平上的中等相互作用粒子系统。主要障碍之一是为具有奇异相互作用的粒子系统建立SDE的强大良好性。为此，我们将结果扩展到Krylov和Röckner\ cite {Kr-ro}的强大良好性，并将其加热核估计的混合$ l^p $ drifts的情况。此外，当相互作用内核被界定时，我们还获得了强收敛的最佳速率，该速率部分基于Jabin和Wang的熵方法\ cite \ cite {JW16}和Zvonkin的转换。
In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular $L^p$-interactions as well as for the moderate interaction particle systems on the level of particle trajectories. One of the main obstacles is to establish the strong well-posedness of the SDEs for particle systems with singular interaction. To this end, we extend the results on strong well-posedness of Krylov and Röckner \cite{Kr-Ro} to the case of mixed $L^p$-drifts, where the heat kernel estimates play a crucial role. Moreover, when the interaction kernel is bounded measurable, we also obtain the optimal rate of strong convergence, which is partially based on Jabin and Wang's entropy method \cite{JW16} and Zvonkin's transformation.
