On the error of Fokker-Planck approximations of some one-step density dependent processes

Abstract

Using operator semigroup methods, we show that Fokker-Planck type secondorder PDE-s can be used to approximate the evolution of the distribution of a one-step process on N particles governed by a large system of ODEs. The error bound is shown to be of order O(1/N ), surpassing earlier results that yielded this order for the error only for the expected value of the process, through mean-field approximations. We also present some conjectures showing that the methods used have the potential to yield even stronger bounds, up to O(1/N 3 ).