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: email@example.com
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
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