Quantitative concentration inequalities on sample path space for mean field interaction
ESAIM: Probability and Statistics, Volume 14  (2010), p. 192-209

We consider the approximation of a mean field stochastic process by a large interacting particle system. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around the law of the process. The method is based on a coupling argument, strong integrability estimates on the paths in Hölder norm, and a general concentration result for the empirical measure of identically distributed independent paths.

DOI : https://doi.org/10.1051/ps:2008033
Classification:  82C22,  35K55,  90C08
Keywords: mean field limits, particle approximation, transportation inequalities
@article{PS_2010__14__192_0,
author = {Bolley, Fran\c cois},
title = {Quantitative concentration inequalities on sample path space for mean field interaction},
journal = {ESAIM: Probability and Statistics},
publisher = {EDP-Sciences},
volume = {14},
year = {2010},
pages = {192-209},
doi = {10.1051/ps:2008033},
zbl = {pre05872992},
mrnumber = {2741965},
language = {en},
url = {http://www.numdam.org/item/PS_2010__14__192_0}
}

Bolley, François. Quantitative concentration inequalities on sample path space for mean field interaction. ESAIM: Probability and Statistics, Volume 14 (2010) , pp. 192-209. doi : 10.1051/ps:2008033. http://www.numdam.org/item/PS_2010__14__192_0/

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