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.

我们提出了一种在给定一系列离散观测值时对多尺度扩散过程进行漂移估计的新方法。对于二尺度势中的朗之万动力学，我们的方法依赖于均质动力学的特征值和特征函数。我们的第一个估计器源自均质扩散过程生成器的鞅估计函数。然而，估计量的无偏性取决于观测值的采样率。因此，我们引入了第二个估计器，它也依赖于数据过滤，并且我们证明它是渐近无偏的，与采样率无关。一系列数值实验说明了我们不同估计器的可靠性和效率。