## Convergence of diffusion-drift many particle systems in probability under a sobolev norm

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, Conference

Liu, JG; Zhang, Y

Published in: Springer Proceedings in Mathematics and Statistics

January 1, 2016

In this paperwedevelop a newmartingale method to showthe 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.

### Duke Scholars

## Published In

Springer Proceedings in Mathematics and Statistics

## DOI

## EISSN

2194-1017

## ISSN

2194-1009

## Publication Date

January 1, 2016

## Volume

162

## Start / End Page

195 / 223

### Citation

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Chicago

ICMJE

MLA

NLM

Liu, J. G., & Zhang, Y. (2016). Convergence of diffusion-drift many particle systems in probability under a sobolev norm. In

*Springer Proceedings in Mathematics and Statistics*(Vol. 162, pp. 195–223). https://doi.org/10.1007/978-3-319-32144-8_10Liu, J. G., and Y. Zhang. “Convergence of diffusion-drift many particle systems in probability under a sobolev norm.” In

*Springer Proceedings in Mathematics and Statistics*, 162:195–223, 2016. https://doi.org/10.1007/978-3-319-32144-8_10.Liu JG, Zhang Y. Convergence of diffusion-drift many particle systems in probability under a sobolev norm. In: Springer Proceedings in Mathematics and Statistics. 2016. p. 195–223.

Liu, J. G., and Y. Zhang. “Convergence of diffusion-drift many particle systems in probability under a sobolev norm.”

*Springer Proceedings in Mathematics and Statistics*, vol. 162, 2016, pp. 195–223.*Scopus*, doi:10.1007/978-3-319-32144-8_10.Liu JG, Zhang Y. Convergence of diffusion-drift many particle systems in probability under a sobolev norm. Springer Proceedings in Mathematics and Statistics. 2016. p. 195–223.

## Published In

Springer Proceedings in Mathematics and Statistics

## DOI

## EISSN

2194-1017

## ISSN

2194-1009

## Publication Date

January 1, 2016

## Volume

162

## Start / End Page

195 / 223