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Quantitative concentration inequalities onsample path space for mean field interaction

Published online by Cambridge University Press:  29 July 2010

François Bolley
François Bolley*
Affiliation:
Université Paris-Dauphine, Ceremade, UMR 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
*
bolley@ceremade.dauphine.fr
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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.

Keywords

Mean field limitsparticle approximationtransportation inequalities

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 192 - 209
Copyright
© EDP Sciences, SMAI, 2010

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