A novel numerical method for McKean-Vlasov stochastic differential equation

In this paper, we propose a novel method to approximate the McKean-Vlasov stochastic differential equation by means of approximating the density function via the Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation whose solution is an approximation to the density function of the solution to the McKean-Vlasov stochastic differential equation. We also apply the finite difference method to approximate the truncated Fokker-Planck equation and derive error estimates. We use the numerical density function to replace the true measure in a McKean-Vlasov stochastic differential equation and set up a stochastic differential equation to approximate the McKean-Vlasov one. Meanwhile, we derive the corresponding error estimates. Finally, we present several numerical experiments to illustrate the theoretical analysis.