Concentration Inequalities for Mean Field Particle Models
DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
RIO, Emmanuel
Advanced Learning Evolutionary Algorithms [ALEA]
Laboratoire de Mathématiques de Versailles [LMV]
Advanced Learning Evolutionary Algorithms [ALEA]
Laboratoire de Mathématiques de Versailles [LMV]
DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
RIO, Emmanuel
Advanced Learning Evolutionary Algorithms [ALEA]
Laboratoire de Mathématiques de Versailles [LMV]
< Réduire
Advanced Learning Evolutionary Algorithms [ALEA]
Laboratoire de Mathématiques de Versailles [LMV]
Langue
en
Article de revue
Ce document a été publié dans
The Annals of Applied Probability. 2011, vol. 21, n° 3, p. 1017-1052
Institute of Mathematical Statistics (IMS)
Résumé en anglais
This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of non linear measure valued processes. We combine an ...Lire la suite >
This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of non linear 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.< Réduire
Mots clés en anglais
Concentration inequalities
mean field particle models
measure valued processes
Feynman-Kac semigroups
McKean Vlasov models.
McKean Vlasov models
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