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We propose a novel method for drift estimation of multiscale diffusionprocesses when a sequence of discrete observations is given. For the Langevindynamics in a two-scale potential, our approach relies on the eigenvalues andthe eigenfunctions of the homogenized dynamics. Our first estimator is derivedfrom a martingale estimating function of the generator of the homogenizeddiffusion process. However, the unbiasedness of the estimator depends on therate with which the observations are sampled. We therefore introduce a secondestimator which relies also on filtering the data and we prove that it isasymptotically unbiased independently of the sampling rate. A series ofnumerical experiments illustrate the reliability and efficiency of ourdifferent estimators.

Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions