From the backward kolmogorov pde on the wasserstein space to propagation of chaos for mckean-vlasov sdes.

Summary In this article, we provide some new quantitative estimates for propagation of chaos of non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov. We obtain explicit error estimates, at the level of the trajectories, at the level of the semi-group and at the level of the densities, for the mean-field approximation by systems of interacting particles under mild regularity assumptions on the coefficients. A first order expansion for the difference between the densities of one particle and its mean-field limit is also established. Our analysis relies on the well-posedness of classical solutions to the backward Kolmogorov partial differential equations (PDEs) defined on the strip [0, T ] × R d × P 2 (R d), P 2 (R d) being the Wasserstein space, that is, the space of probability measures on R d with a finite second-order moment and also on the existence and uniqueness of a fundamental solution for the related parabolic linear operator here stated on [0, T ] × P 2 (R d).