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

Jian-Guo Liu Duke University Yuan Zhang Dept. of Mathematics, UCLA

Probability mathscidoc:1702.28003

From Particle Systems to Partial Differential Equations III, 195-223, 2016.1
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.
Many particle system, martingale method, energy-dissipation inequality.
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@inproceedings{jian-guo2016convergence,
  title={Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm},
  author={Jian-Guo Liu, and Yuan Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207214256667663267},
  booktitle={ From Particle Systems to Partial Differential Equations III},
  pages={195-223},
  year={2016},
}
Jian-Guo Liu, and Yuan Zhang. Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm. 2016. In From Particle Systems to Partial Differential Equations III. pp.195-223. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207214256667663267.
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