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
@article{PS_2010__14__192_0, author = {Bolley, Fran\c{c}ois}, title = {Quantitative concentration inequalities on sample path space for mean field interaction}, journal = {ESAIM: Probability and Statistics}, pages = {192--209}, publisher = {EDP-Sciences}, volume = {14}, year = {2010}, doi = {10.1051/ps:2008033}, mrnumber = {2741965}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2008033/} }
TY - JOUR AU - Bolley, François TI - Quantitative concentration inequalities on sample path space for mean field interaction JO - ESAIM: Probability and Statistics PY - 2010 SP - 192 EP - 209 VL - 14 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2008033/ DO - 10.1051/ps:2008033 LA - en ID - PS_2010__14__192_0 ER -
%0 Journal Article %A Bolley, François %T Quantitative concentration inequalities on sample path space for mean field interaction %J ESAIM: Probability and Statistics %D 2010 %P 192-209 %V 14 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2008033/ %R 10.1051/ps:2008033 %G en %F PS_2010__14__192_0
Bolley, François. Quantitative concentration inequalities on sample path space for mean field interaction. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 192-209. doi : 10.1051/ps:2008033. http://www.numdam.org/articles/10.1051/ps:2008033/
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