A novel numerical method for mean field stochastic differential equation
Abstract
In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation whose solution is an approximation to the density function of solution to the mean field stochastic differential equation. We also apply 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 mean field stochastic differential equation and set up a stochastic differential equation to approximate the mean field one. Meanwhile, we derive the corresponding error estimates. Finally, we present several numerical experiments to illustrate the theoretical analysis.
Cite
@article{arxiv.2503.17980,
title = {A novel numerical method for mean field stochastic differential equation},
author = {Jinhui Zhou and Yongkui Zou and Shimin Chai and Boyu Wang and Ziyi Tan},
journal= {arXiv preprint arXiv:2503.17980},
year = {2025}
}