Estimation for stochastic damping hamiltonian systems under partial observation-I. Invariant density

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Cattiaux, Patrick¹  Leon, Jose R.²  Prieur, Clementine³ 

[1] Univ Toulouse, CNRS UMR 5219, Inst Math Toulouse, F-31062 Toulouse 09, France

[2] Cent Univ Venezuela, Fac Ciencias, Escuela Matemat, Caracas 1041 A, Venezuela

[3] Univ Grenoble 1, INRIA MOISE Project Team, Lab Jean Kuntzmann, F-38041 Grenoble, France

关键词: Hypoelliptic diffusion;    Nonparametric density estimation;    Partial observations;   

DOI  :  10.1016/j.spa.2013.10.008

来源: Elsevier

【 摘 要 】

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 co-variance 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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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