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

Abstract

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.