Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term
Abstract
This paper is the third part of our study started with Cattiaux, Le\'{o}n 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.
Cite
@article{arxiv.1606.06934,
title = {Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term},
author = {Patrick Cattiaux and José R. León and Clémentine Prieur},
journal= {arXiv preprint arXiv:1606.06934},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/15-AAP1126 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)