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June 2016 Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term
Patrick Cattiaux, José R. León, Clémentine Prieur
Ann. Appl. Probab. 26(3): 1581-1619 (June 2016). DOI: 10.1214/15-AAP1126

Abstract

This paper is the third part of our study started with Cattiaux, León 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.

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Patrick Cattiaux. José R. León. Clémentine Prieur. "Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term." Ann. Appl. Probab. 26 (3) 1581 - 1619, June 2016. https://doi.org/10.1214/15-AAP1126

Information

Received: 1 July 2014; Revised: 1 May 2015; Published: June 2016
First available in Project Euclid: 14 June 2016

zbMATH: 1343.62047
MathSciNet: MR3513599
Digital Object Identifier: 10.1214/15-AAP1126

Subjects:
Primary: 62M05
Secondary: 35H10 , 60F05 , 60H10

Keywords: fluctuation-dissipation models , Hypoelliptic diffusion , variance estimation

Rights: Copyright © 2016 Institute of Mathematical Statistics

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