Dimension-independent L^p convergence rate of propagation of chaos and numerical analysis for McKean-Vlasov stochastic differential equations

In this paper, we mainly study the L^p convergence rate of propagation of chaos (PoC) for McKean-Vlasov stochastic differential equations (MV-SDEs) with coefficients nonlinearly depending on the measure. The optimal strong PoC convergence rate N^−1/2 is well established for MV-SDEs with coefficients linearly depending on the measure, whereas the rate deteriorates with the dimension d for coefficients that are Lipschitz continuous with respect to the measure. In this work, we prove the optimal PoC rate, in the sense of L^p for any p ≥ 2, for two classes of MV-SDEs whose coefficients are Lipschitz continuous but nonlinearly dependent on the measure component. By employing the conditional Rosenthal inequality, we establish the optimal rate, bypassing the need to consider the Wasserstein distance between the empirical measure and its limiting distribution. As a complement, we further provide a time discretization scheme for the equations and verify the PoC convergence rate through several numerical experiments.