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2016 | OriginalPaper | Chapter

Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm

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Abstract

In this paper we develop a new martingale method to show the convergence of the regularized empirical measure of many particle systems in probability under a Sobolev norm to the corresponding mean field PDE. Our method works well for the simple case of Fokker Planck equation and we can estimate a lower bound of the rate of convergence. This method can be generalized to more complicated systems with interactions.

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Metadata
Title
Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm
Authors
Jian-Guo Liu
Yuan Zhang
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-32144-8_10

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