The Least Squares Estimation for the α-Stable Ornstein-Uhlenbeck Process with Constant Drift

In this paper, we consider the least squares estimators of the Ornstein-Uhlenbeck process with a constant drift dXt=(θ1−θ2Xt)dt+dZt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$dX_{t}=(\theta_{1}-\theta_{2}X_{t})dt+dZ_{t} $$\end{document}with X0 = x0, where θ1, θ2 are two unknown parameters with θ2 > 0 and Z is a strictly symmetric α-stable motion on ℝ with the index α ∈ (1, 2). We construct the least squares estimators of θ1 and θ2 based on the discrete observation, and discuss the strong consistency and asymptotic distributions of the two estimators. Finally, we give some numerical calculus and simulations.