Differential and Integral Equations
- Differential Integral Equations
- Volume 33, Number 1/2 (2020), 67-90.
On the error of Fokker-Planck approximations of some one-step density dependent processes
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 $O(1/N^3)$.
Differential Integral Equations, Volume 33, Number 1/2 (2020), 67-90.
First available in Project Euclid: 6 February 2020
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q84: Fokker-Planck equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N40: Applications in numerical analysis [See also 65Jxx] 60J28: Applications of continuous-time Markov processes on discrete state spaces
Kunszenti-Kovács, Dávid. On the error of Fokker-Planck approximations of some one-step density dependent processes. Differential Integral Equations 33 (2020), no. 1/2, 67--90. https://projecteuclid.org/euclid.die/1580958030