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arXiv · 1606.06934

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

Patrick Cattiaux·José R. León·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.

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Patrick Cattiaux, José R. León, Clémentine Prieur. 2016-06-22. Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term. https://doi.org/10.1214/15-aap1126

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