A1439
Title: Estimation of the invariant measure of a multidimensional diffusion from noisy observations
Authors: Gregoire Szymanski - Université du Luxembourg, DMATH (France) [presenting]
Raphael Maillet - Universite Paris-Dauphine (France)
Abstract: The purpose is to present a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations that are blurred by independent noise. The focus is on the intermediate regime, where observations are collected at discrete times $k\Delta_n$ for $k=0,\dots,n$, under the conditions $\Delta_n \to 0$ and $n\Delta_n \to \infty$. The method relies on a kernel density estimator combined with a pre-averaging technique, which effectively removes noise from the data while preserving the analytical structure of the underlying signal and its asymptotic behavior. How the rate of convergence of the estimator depends on both the anisotropic regularity of the density and the noise intensity is discussed. In particular, conditions on the noise level that allow achieving convergence rates comparable to the noiseless case are described.
