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.
CITATION STYLE
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). Springer New York LLC. https://doi.org/10.1007/978-3-319-32144-8_10
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