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| HAL : hal-00686272, version 1 |
| arXiv : 1204.1922 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (09-04-2012) | v2 (17-09-2012) | v3 (19-09-2012) | v4 (06-12-2012) |
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| Quantitative ergodicity for some switched dynamical systems |
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| Michel Benaïm 1Stéphane Le Borgne 2 |
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| (04/2012) |
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| We provides quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continous component evolves according to a smooth vector field that it switched at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. |
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| 1 : | Institut de Mathématiques (UNINE) |
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Université de Neuchatel |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3 : | Institut de Mathématiques de Bourgogne (IMB) |
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CNRS : UMR5584 – Université de Bourgogne |
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| Théorie ergodique Processus stochastiques |
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| Domaine | : | Mathématiques/Probabilités |
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| Coupling – Ergodicity – Linear Differential Equations – Piecewise Deterministic Markov Process – Switched dynamical systems – Wasserstein distance |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00686272, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00686272 | |
| oai:hal.archives-ouvertes.fr:hal-00686272 | |
| Contributeur : Pierre-André Zitt | |
| Soumis le : Lundi 9 Avril 2012, 16:12:47 | |
| Dernière modification le : Lundi 10 Septembre 2012, 10:23:57 | |
