ESTIMATION FOR STOCHASTIC DAMPING HAMILTONIAN SYSTEMS UNDER PARTIAL OBSERVATION. III. DIFFUSION TERM

• 成果类型: Article
• 署名作者: Cattiaux, Patrick; Leon, Jose R.; Prieur, Clementine
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Central Venezuela; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1126
• 发表日期: 2016
• 页码: 1581-1619
• 关键词: parameter-estimation; MARKOV-PROCESSES; LIMIT-THEOREMS; CONVERGENCE; SEMIMARTINGALES; functionals; coefficient; DYNAMICS; models

摘要

This paper is the third part of our study started with Cattiaux, Leon and Prieur [Stochastic Process. Appl. 124 (2014) 1236-1260; ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 359-384]. For some ergodic Hamiltonian systems, we obtained a central limit theorem for a nonparametric estimator of the invariant density [Stochastic Process. Appl. 124 (2014) 1236-1260] and of the drift term [ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 359-384], under partial observation (only the positions are observed). Here, we obtain similarly a central limit theorem for a nonparametric estimator of the diffusion term.