Estimation for stochastic damping Hamiltonian systems under partial observation. III. Diffusion term
نویسندگان
چکیده
This paper is the third part of our study started with Cattiaux, León and Prieur (2014 2013). For some ergodic hamiltonian systems we obtained a central limit theorem for a non-parametric estimator of the invariant density (Cattiaux et al. 2014) and of the drift term (Cattiaux et al. 2013), under partial observation (only the positions are observed). Here we obtain similarly a central limit theorem for a non-parametric estimator of the diffusion term.
منابع مشابه
Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. II Drift term
This paper is the second part of our study started with Cattiaux et al. (2014). For some ergodic hamiltonian systems we obtained a central limit theorem for a non-parametric estimator of the invariant density, under partial observation (only the positions are observed). Here we obtain similarly a central limit theorem for a non-parametric estimator of the drift term. This theorem relies on the ...
متن کاملEstimation for Stochastic Damping Hamiltonian Systems under Partial Observation. I. Invariant density
In this paper, we study the non-parametric estimation of the invariant density of some ergodic hamiltonian systems, using kernel estimators. The main result is a central limit theorem for such estimators under partial observation (only the positions are observed). The main tools are mixing estimates and refined covariance inequalities, the main difficulty being the strong degeneracy of such pro...
متن کاملRecursive Estimation for Stochastic Damping Hamiltonian Systems
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...
متن کاملAdaptive Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation
The paper considers a process Zt = (Xt, Yt) where Xt is the position of a particle and Yt its velocity, driven by a hypoelliptic bi-dimensional stochastic differential equation. Under adequate conditions, the process is stationary and geometrically β-mixing. In this context, we propose an adaptive non-parametric kernel estimator of the stationary density p of Z, based on n discrete time observa...
متن کاملAlmost sure exponential stability of stochastic reaction diffusion systems with Markovian jump
The stochastic reaction diffusion systems may suffer sudden shocks, in order to explain this phenomena, we use Markovian jumps to model stochastic reaction diffusion systems. In this paper, we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps. Under some reasonable conditions, we show that the trivial solution of stocha...
متن کامل