The Annals of Applied Probability

Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term

Patrick Cattiaux, José R. León, and Clémentine Prieur

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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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1581-1619.

Dates
Received: July 2014
Revised: May 2015
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1465905012

Digital Object Identifier
doi:10.1214/15-AAP1126

Mathematical Reviews number (MathSciNet)
MR3513599

Zentralblatt MATH identifier
1343.62047

Subjects
Primary: 62M05: Markov processes: estimation
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60F05: Central limit and other weak theorems 35H10: Hypoelliptic equations

Keywords
Hypoelliptic diffusion variance estimation fluctuation-dissipation models

Citation

Cattiaux, Patrick; León, José R.; Prieur, Clémentine. Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term. Ann. Appl. Probab. 26 (2016), no. 3, 1581--1619. doi:10.1214/15-AAP1126. https://projecteuclid.org/euclid.aoap/1465905012


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