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| HAL: inria-00375134, version 2 |
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| Available versions | v1 (2009-04-14) | v2 (2009-04-14) | v3 (2009-04-26) |
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| Concentration Inequalities for Mean Field Particle Models |
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Pierre Del Moral 1, 2Emmanuel Rio 2, 3 |
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| (2009) |
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| 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. |
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| 1: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 2: | ALEA (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université de Bordeaux – CNRS : UMR5251 |
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| 3: | Laboratoire de Mathématiques de Versailles (LM-Versailles) |
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CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines |
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| Domain | : | Mathematics/Probability |
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| Concentration inequalities – mean field particle models – measure valued processes – Feynman-Kac semigroups – McKean Vlasov models. |
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| inria-00375134, version 2 | |
| http://hal.inria.fr/inria-00375134 | |
| oai:hal.inria.fr:inria-00375134 | |
| From: Pierre Del Moral | |
| Submitted on: Tuesday, 14 April 2009 15:30:50 | |
| Updated on: Tuesday, 14 April 2009 15:53:24 | |
