## Differential and Integral Equations

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

Dávid Kunszenti-Kovács

#### Abstract

Using operator semigroup methods, we show that Fokker-Planck type second-order PDEs 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 $O(1/N^3)$.

#### Article information

Source
Differential Integral Equations, Volume 33, Number 1/2 (2020), 67-90.

Dates
First available in Project Euclid: 6 February 2020