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June 2011 Concentration inequalities for mean field particle models
Pierre Del Moral, Emmanuel Rio
Ann. Appl. Probab. 21(3): 1017-1052 (June 2011). DOI: 10.1214/10-AAP716

Abstract

This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic perturbation analysis with a concentration analysis for triangular arrays of conditionally independent random sequences, which may be of independent interest. Under some additional stability properties of the limiting measure valued processes, uniform concentration properties, with respect to the time parameter, are also derived. The concentration inequalities presented here generalize the classical Hoeffding, Bernstein and Bennett inequalities for independent random sequences to interacting particle systems, yielding very new results for this class of models.

We illustrate these results in the context of McKean–Vlasov-type diffusion models, McKean collision-type models of gases and of a class of Feynman–Kac distribution flows arising in stochastic engineering sciences and in molecular chemistry.

Citation

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Pierre Del Moral. Emmanuel Rio. "Concentration inequalities for mean field particle models." Ann. Appl. Probab. 21 (3) 1017 - 1052, June 2011. https://doi.org/10.1214/10-AAP716

Information

Published: June 2011
First available in Project Euclid: 2 June 2011

zbMATH: 1234.60019
MathSciNet: MR2830611
Digital Object Identifier: 10.1214/10-AAP716

Subjects:
Primary: 60E15 , 60K35
Secondary: 60F10 , 60F99 , 82C22

Keywords: Concentration inequalities , Feynman–Kac semigroups , McKean–Vlasov models , mean field particle models , measure valued processes

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 3 • June 2011
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