Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley

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.

Mots clés: Mean field limits; particle approximation; transportation inequalities

François Bolley. Quantitative concentration inequalities on sample path space for mean field interaction. ESAIM: Probability and Statistics, 2010, 14, pp.192-209. ⟨10.1051/ps:2008033⟩. ⟨hal-00612392⟩