A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations (Q1872347)

The authors study McKean-Vlasov equations with random initial conditions. They give a probabilistic representation of the moments of the solutions in order to approximate them by a stochastic particle method. This method is based on random weights which are defined through nonparametric estimators of a regression function. It is both original and efficient, and the convergence rate is estimated in terms of the number of simulated particles and the time discretization step. Singular interactions as in Burgers equation or Navier-Stokes equations are unfortunately not in the scope of this work.