Approximations of McKean-Vlasov Stochastic Differential Equations with Irregular Coefficients

The goal of this paper is to approximate two kinds of McKean-Vlasov stochastic differential equations (SDEs) with irregular coefficients via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler-Maruyama scheme associated with the consequent weakly interacting particle systems are investigated for McKean-Vlasov SDEs, where (1) the diffusion terms are Holder continuous by taking advantage of Yamada-Watanabe's approximation approach and (2) the drifts are Holder continuous by freezing distributions followed by invoking Zvonkin's transformation trick.