离散观测多尺度扩散漂移估计的特征函数鞅估计函数和滤波数据
Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions
摘要：
提出了一种新的多尺度扩散过程的漂移估计方法。对于双尺度势中的朗之万动力学，我们的方法依赖于均匀化动力学的本征值和本征函数。我们的第一个估计是由均匀化扩散过程的生成元的鞅估计函数导出的。然而，估计量的无偏性取决于对观测值进行采样的速率。因此，我们引入了第二个估计也依赖于过滤的数据，我们证明了它是独立的采样率渐近无偏。一系列的数值实验说明了我们不同的估计的可靠性和效率。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
