Iterative Multilevel density estimation for McKean-Vlasov SDEs via projections

Abstract

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.

22 pages, 10 figures

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