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

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From Particle Systems to Partial Differential Equations III

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 162))

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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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Acknowledgments

The research was partially supported by KI-Net NSF RNMS Grant No. 1107291, and NSF DMS Grant No. 1514826.

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Authors and Affiliations

  1. Department of Physics and Department of Mathematics, Duke University, 90320, Durham, NC, 27708-0320, USA

    Jian-Guo Liu

  2. Department of Mathematics, University of California, Los Angeles, 951555, Los Angeles, CA, 90095-1555, USA

    Yuan Zhang

Authors
  1. Jian-Guo Liu
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  2. Yuan Zhang
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Corresponding author

Correspondence to Jian-Guo Liu .

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Editors and Affiliations

  1. University of Minho Department of Mathematics, Braga, Portugal

    Patrícia Gonçalves

  2. University of Minho Department of Mathematics, Braga, Portugal

    Ana Jacinta Soares

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Liu, JG., Zhang, Y. (2016). Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations III. Springer Proceedings in Mathematics & Statistics, vol 162. Springer, Cham. https://doi.org/10.1007/978-3-319-32144-8_10

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