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Author: Belomestny, Denis × Subject: particle systems ×

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    Projected particle methods for solving McKean-Vlasov equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Belomestny, Denis; Schoenmakers, John G.M.
    We study a novel projection-based particle method to the solution of the corresponding McKean-Vlasov equation. Our approach is based on the projection-type estimation of the marginal density of the solution in each time step. The projection-based particle method can profit from additional smoothness of the underlying density and leads in many situation to a signficant reduction of numerical complexity compared to kernel density estimation algorithms. We derive strong convergence rates and rates of density estimation. The case of linearly growing coefficients of the McKean-Vlasov equation turns out to be rather challenging and requires some new type of averaging technique. This case is exemplified by explicit solutions to a class of McKean-Vlasov equations with affine drift.