Differential and Integral Equations

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

Dávid Kunszenti-Kovács

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1580958030

Mathematical Reviews number (MathSciNet)
MR4060435

Zentralblatt MATH identifier
07177895

Subjects
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

Citation

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


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