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mean field limits

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1 results

Quantitative concentration inequalities onsample path space for mean field interaction
François Bolley
Journal:

ESAIM: Probability and Statistics / Volume 14 / 2010

Published online by Cambridge University Press:

29 July 2010, pp. 192-209

Print publication:

2010
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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.