Iterative Multilevel density estimation for McKean-Vlasov SDEs via projections
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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 <cit.> with non-interacting kernels and projection estimation of particle densities <cit.>. By exploiting smoothness of the coefficients for McKean-Vlasov SDEs, in the best case scenario (i.e C^∞ for the coefficients), we obtain the complexity of order O(ϵ^-2|logϵ|^4) for the approximation of expectations and O(ϵ^-2|logϵ|^5) for density estimation.
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