A higher order weak approximation of McKean-Vlasov type SDEs

The paper introduces a new weak approximation algorithm for stochastic differential equations (SDEs) of McKean-Vlasov type. The arbitrary order discretization scheme is available and is given using Malliavin weights, certain polynomial weights of Brownian motion, which play a role as correction of the approximation. The new weak approximation scheme works even if the test function is not smooth. In other words, the expectation of irregular functionals of McKean-Vlasov SDEs such as probability distribution functions are approximated through the proposed scheme. The effectiveness of the higher order scheme is confirmed by numerical examples for McKean-Vlasov SDEs including the Kuramoto model.