hal-00739136, version 1
Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. I. Invariant density.
Patrick Cattiaux
1Jose R. Leon 2Clémentine Prieur 3
(05/10/2012)
Résumé : In this paper, we study the non-parametric estimation of the invariant density of some ergodic hamiltonian systems, using kernel estimators. The main result is a central limit theorem for such estimators under partial observation (only the positions are observed). The main tools are mixing estimates and refined covariance inequalities, the main difficulty being the strong degeneracy of such processes. This is the first paper of a series of at least two, devoted to the estimation of the characteristics of such processes: invariant density, drift term, volatility ....
- 1 : Institut de Mathématiques de Toulouse (IMT)
- Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219
- 2 : Universidad Central de Venezuela
- Universidad Central de Venezuela
- 3 : MOISE (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
- CNRS : UMR5224 – INRIA – Laboratoire Jean Kuntzmann – Université Joseph Fourier - Grenoble I – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
- Collaboration : ECOS-Nord program for French- Venezuelian Scientific Cooperation (V12M01 project)
- Domaine : Mathématiques/Statistiques
Statistiques/Théorie - Mots-clés : hypoelliptic diffusion – nonparametric density estimation – partial observations
- hal-00739136, version 1
- http://hal.archives-ouvertes.fr/hal-00739136
- oai:hal.archives-ouvertes.fr:hal-00739136
- Contributeur : Clémentine Prieur
- Soumis le : Vendredi 5 Octobre 2012, 18:38:16
- Dernière modification le : Vendredi 5 Octobre 2012, 21:19:21
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