Abstract

In this talk, we introduce a new weak approximation algorithm for McKean-Vlasov (MKV) stochastic differential equation (SDE) based on the particle method and Malliavin calculus. The proposed method gives arbitrary order time discretization which requires minimum cost on random number generation as in the standard particle method for MKV SDEs. Moreover, it works even if the test function is not smooth. In other words, the expectations of irregular functionals of MKV SDEs such as probability distribution functions are approximated through the proposed scheme. The numerical results for MKV SDEs confirm the validity of the scheme.
This talk is based on the joint work with Toshihiro Yamada.