A New Approximate Method to Mean Field Stochastic Differential Equation with One-Sided Lipschitz Drift Coefficient

Abstract

In this paper, we construct a numerical method to approximate a class of mean field stochastic differential equations whose drift coefficient satisfies a one-sided Lipschitz condition. The key idea is to independently approximate the distribution via solving a nonlinear Fokker-Planck equation which governs the density function of the solution. Meanwhile, based on the approximate density function, we construct an approximate stochastic differential equation to approach the mean field one. Then, we also apply a truncated Euler-Maruyama method to achieve discretization and derive error estimates. Finally, we present several numerical experiments to illustrate our theoretical analysis.