Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

RATE OF ESTIMATION FOR THE STATIONARY DISTRIBUTION OF STOCHASTIC DAMPING HAMILTONIAN SYSTEMS WITH CONTINUOUS OBSERVATIONS

Abstract : We study the problem of the non-parametric estimation for the density π of the stationary distribution of a stochastic two-dimensional damping Hamiltonian system (Z_t) t∈[0,T ] = (X_t, Y_t) t∈[0,T ]. From the continuous observation of the sampling path on [0, T ], we study the rate of estimation for π(x_0 , y_0) as T → ∞. We show that kernel based estimators can achieve the rate T^{−v} for some explicit exponent v ∈ (0, 1/2). One finding is that the rate of estimation depends on the smoothness of π and is completely different with the rate appearing in the standard i.i.d. setting or in the case of two-dimensional non degenerate diffusion processes. Especially, this rate depends also on y 0. Moreover, we obtain a minimax lower bound on the L 2-risk for pointwise estimation, with the same rate T^{−v}, up to log(T) terms.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02455744
Contributor : Arnaud Gloter <>
Submitted on : Sunday, January 26, 2020 - 4:55:10 PM
Last modification on : Monday, April 6, 2020 - 4:53:59 PM
Document(s) archivé(s) le : Monday, April 27, 2020 - 4:30:14 PM

Files

stationary_hypo_v7_HaL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02455744, version 1
  • ARXIV : 2001.10423

Citation

Sylvain Delattre, Arnaud Gloter, Nakahiro Yoshida. RATE OF ESTIMATION FOR THE STATIONARY DISTRIBUTION OF STOCHASTIC DAMPING HAMILTONIAN SYSTEMS WITH CONTINUOUS OBSERVATIONS. 2020. ⟨hal-02455744⟩

Share

Metrics

Record views

79

Files downloads

38