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| HAL : hal-00355211, version 8 |
| arXiv : 0901.3476 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (22-01-2009) | v2 (02-03-2009) | v3 (06-03-2009) | v4 (06-04-2009) | v5 (24-06-2009) | v6 (21-10-2009) | v7 (15-10-2010) | v8 (29-11-2011) |
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| Expansion of the propagation of chaos for Bird and Nanbu systems. |
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| Sylvain Rubenthaler 1 |
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| (13/11/2011) |
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| The Bird and Nanbu systems are particle systems used to approximate the solution of the mollied Boltzmann equation. In particular, they have the propagation of chaos property. Following [GM94, GM97, GM99], we use coupling techniques and results on branching processes to write an expansion of the error in the propagation of chaos in terms of the number of particles, for slightly more general systems than the ones cited above. This result leads to the proof of the a.s convergence and the centrallimit theorem for these systems. In particular, we have a central-limit theorem for the empirical measure of the system under less assumptions then in [Mél98]. As in [GM94, GM97, GM99], these results apply to the trajectories of particles on an interval [0; T]. |
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| 1 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
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| Domaine | : | Mathématiques/Probabilités |
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| interacting particle systems – Boltzmann equation – nonlinear diffusion with jumps – random graphs and trees – coupling – propagation of chaos – Monte Carlo algorithm |
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| hal-00355211, version 8 | |
| http://hal.archives-ouvertes.fr/hal-00355211 | |
| oai:hal.archives-ouvertes.fr:hal-00355211 | |
| Contributeur : Sylvain Rubenthaler | |
| Soumis le : Mardi 29 Novembre 2011, 11:53:06 | |
| Dernière modification le : Mardi 29 Novembre 2011, 13:40:19 | |
