Issue |
ESAIM: PS
Volume 14, 2010
|
|
---|---|---|
Page(s) | 192 - 209 | |
DOI | https://doi.org/10.1051/ps:2008033 | |
Published online | 29 July 2010 |
Quantitative concentration inequalities on sample path space for mean field interaction
Université Paris-Dauphine, Ceremade, UMR 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Corresponding author: bolley@ceremade.dauphine.fr
Received:
3
April
2008
Revised:
29
September
2008
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.
Mathematics Subject Classification: 82C22 / 35K55 / 90C08
Key words: Mean field limits / particle approximation / transportation inequalities
© EDP Sciences, SMAI, 2010
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