WIAS Preprint No. 2341, (2016)

Projected particle methods for solving McKean--Vlaslov equations


Authors

  • Belomestny, Denis
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2010 Mathematics Subject Classification

  • 60H10 60K35

Keywords

  • McKean-Vlaslov equations, particle systems, projection estimators, explicit solutions

DOI

10.20347/WIAS.PREPRINT.2341

Abstract

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 significant 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.

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