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B0462
**Title: **Rate of estimation for the stationary distribution of stochastic damping Hamiltonian systems with continuous observation
**Authors: **Arnaud Gloter - Universite d Evry Val d Essonne (France) **[presenting]**

Nakahiro Yoshida - University of Tokyo (Japan)

Sylvain Delattre - University Paris Diderot (France)

**Abstract: **The problem of the non-parametric estimation of the stationary measure $\pi$ of a stochastic two dimensional damping Hamiltonian system $(Z_t)_{t\in[0,T]}=(X_t,Y_t)_{t \in [0,T]}$ is studied. From the observation of the path on $[0,T]$ we determine the rate of estimation of $\pi(x_0,y_0)$ as $T \to \infty$ : we obtain a minimax lower bound on the estimation risk for pointwise estimation, and we show that this lower bound can be obtained by some estimators. One finding is that the rate of estimation is different with the one appearing in the standard i.i.d. setting or in the case of two dimensional non degenerate diffusion processes.

Nakahiro Yoshida - University of Tokyo (Japan)

Sylvain Delattre - University Paris Diderot (France)