Recursive Estimation for Stochastic Damping Hamiltonian Systems

Patrick Cattiaux 1 José R. Leon 2 Clémentine Prieur 3, 4
4 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : In this paper, we complete our previous works (Cattiaux, Leon and Prieur, 2014-a, b and c) on the (non-parametric) estimation of the characteristics (invariant density, drift term,variance term) of some ergodic hamiltonian systems, under partial observations. More precisely, we introduce recursive estimators using the full strength of the ergodic behavior. We compare the theoretical results obtained with these estimators to the results we proved for the ones we have introduced previously.
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Patrick Cattiaux, José R. Leon, Clémentine Prieur. Recursive Estimation for Stochastic Damping Hamiltonian Systems. Journal of Nonparametric Statistics, American Statistical Association, 2015, 27 (3), pp.401-424. ⟨10.1080/10485252.2015.1046451⟩. ⟨hal-01071252⟩

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