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.

翻译：我们建议了一种新颖的方法,用于在进行一系列离散观测时对多尺度扩散过程进行漂移估计。对于两种规模的Langevin动力学,我们的方法依赖于同质动力学的精华值和元功能。我们的第一个估计值来自同质扩散过程的生成者的马丁格估计功能。然而,估计值的公正性取决于观测的抽样率。因此,我们引入了第二个估计器,它也依赖于对数据的过滤,我们证明它与取样率无关,是无差别的。一系列数字实验显示了我们不同估计值的可靠性和效率。