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arXiv · 1612.08829

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 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 $O(1/N^3)$.

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Dávid Kunszenti-Kovács. 2016-12-28. On the error of Fokker-Planck approximations of some one-step density dependent processes. https://arxiv.org/abs/1612.08829

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