In this paper, we present a generic methodology for the efficient numerical approximation of the density function of the McKean-Vlasov SDEs. The weak error analysis for the projected process motivates us to combine the iterative Multilevel Monte Carlo method for McKean-Vlasov SDEs \cite{ szpruch2019} with non-interacting kernels and projection estimation of particle densities \cite{ belomestny2018projected}. By exploiting smoothness of the coefficients for McKean-Vlasov SDEs, in the best case scenario (i.e $C^{ \infty}$ for the coefficients), we obtain the complexity of order $O(\epsilon^{ -2}|\log\epsilon|^4)$ for the approximation of expectations and $O(\epsilon^{ -2}|\log\epsilon|^5)$ for density estimation.
Categories: math.NA cs.NA math.PR