带交互项的Ornstein-Uhlenbeck过程的轨迹拟合估计

Trajectory Fitting Estimator for the Ornstein-Uhlenbeck Processes with Self-Interacting Drift

在本文中,我们研究带自排斥漂移项的非遍历的Ornstein-Uhlenbeck过程的参数估计问题其中ZT是α-stable Lévy过程,θ>0是未知参数。我们讨论当T→∞,基于连续观测下的θ的加权轨迹拟合参数θ ^T的相合性和渐近分布。

In this paper, we consider parameter estimation problem for the non-ergodic Ornstein-Uhlenbeck processes with self-interacting drift where ZT is an α-stable Lévy motion with θ>0 is an unknown parameter. We consider the consistency and the asymptotic distributions of the weighted trajectory fitting estimator θ ^T of θ based on the continuous observation as T→∞ .