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Quantitative concentration inequalities on sample path space for mean field interaction

Bolley, François (2010), Quantitative concentration inequalities on sample path space for mean field interaction, ESAIM. Probability and Statistics, 14, p. 192-209. http://dx.doi.org/10.1051/ps:2008033

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Type
Article accepté pour publication ou publié
Date
2010
Journal name
ESAIM. Probability and Statistics
Volume
14
Publisher
Cambridge University Press
Pages
192-209
Publication identifier
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Author(s)
Bolley, François
Abstract (EN)
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.
Subjects / Keywords
Mean field limits; particle approximation; transportation inequalities