Projected particle methods for solving McKean--Vlaslov equations
- Belomestny, Denis
- Schoenmakers, John G. M.
2010 Mathematics Subject Classification
- 60H10 60K35
- McKean-Vlaslov equations, particle systems, projection estimators, explicit solutions
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.