  We propose a novel method for drift estimation of multiscale diffusion
processes when a sequence of discrete observations is given. For the Langevin
dynamics in a two-scale potential, our approach relies on the eigenvalues and
the eigenfunctions of the homogenized dynamics. Our first estimator is derived
from a martingale estimating function of the generator of the homogenized
diffusion process. However, the unbiasedness of the estimator depends on the
rate with which the observations are sampled. We therefore introduce a second
estimator which relies also on filtering the data and we prove that it is
asymptotically unbiased independently of the sampling rate. A series of
numerical experiments illustrate the reliability and efficiency of our
different estimators.

Numerical Analysis;Numerical Analysis