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January/February 2020 On the error of Fokker-Planck approximations of some one-step density dependent processes
Dávid Kunszenti-Kovács
Differential Integral Equations 33(1/2): 67-90 (January/February 2020).

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 $O(1/N^3)$.

Citation

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Dávid Kunszenti-Kovács. "On the error of Fokker-Planck approximations of some one-step density dependent processes." Differential Integral Equations 33 (1/2) 67 - 90, January/February 2020.

Information

Published: January/February 2020
First available in Project Euclid: 6 February 2020

zbMATH: 07177895
MathSciNet: MR4060435

Subjects:
Primary: 35Q84, 47D06, 47N40, 60J28

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.33 • No. 1/2 • January/February 2020
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