Quantitative concentration inequalities on sample path space for mean field interaction
ESAIM: Probability and Statistics, Tome 14 (2010), pp. 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 : 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{c}ois},
     title = {Quantitative concentration inequalities on sample path space for mean field interaction},
     journal = {ESAIM: Probability and Statistics},
     pages = {192--209},
     year = {2010},
     publisher = {EDP Sciences},
     volume = {14},
     doi = {10.1051/ps:2008033},
     mrnumber = {2741965},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps:2008033/}
}
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Bolley, François. Quantitative concentration inequalities on sample path space for mean field interaction. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 192-209. doi: 10.1051/ps:2008033

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