Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 192-209
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Bolley, François. "Quantitative concentration inequalities on sample path space for mean field interaction." ESAIM: Probability and Statistics 14 (2010): 192-209. <http://eudml.org/doc/250821>.

@article{Bolley2010,
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. },
author = {Bolley, François},
journal = {ESAIM: Probability and Statistics},
keywords = {Mean field limits; particle approximation; transportation inequalities; mean field limits},
language = {eng},
month = {7},
pages = {192-209},
publisher = {EDP Sciences},
title = {Quantitative concentration inequalities on sample path space for mean field interaction},
url = {http://eudml.org/doc/250821},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Bolley, François
TI - Quantitative concentration inequalities on sample path space for mean field interaction
JO - ESAIM: Probability and Statistics
DA - 2010/7//
PB - EDP Sciences
VL - 14
SP - 192
EP - 209
AB - 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.
LA - eng
KW - Mean field limits; particle approximation; transportation inequalities; mean field limits
UR - http://eudml.org/doc/250821
ER -

References

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