Propagation of Chaos for Derivatives of McKean-Vlasov Stochastic Differential Equations and Applications

Abstract: As an enhanced version of existing results on Kac's propagation of chaos, which describes the convergence of mean-field particle systems to the independent McKean-Vlasov particle system as the number of particles tends to infinity, we prove the convergence at the level of derivatives with respect to the perturbations of initial value and noise, together with explicit convergence rates that can be sharp. As a consequence, the intrinsic derivative for the distribution of a single particle converges to that of an independent McKean-Vlasov SDE.