Least squares estimator for Ornstein–Uhlenbeck processes driven by fractional Lévy processes from discrete observations

In this paper, we consider the problem of parameter estimation for Ornstein–Uhlenbeck processes with small fractional Lévy noises, based on discrete observations at n regularly spaced time points ti=i/n,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_i=i/n,$$\end{document}i=1,…,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i=1,\ldots ,n$$\end{document} on [0, 1]. Least squares method is used to obtain an estimator of the drift parameter. The consistency and the asymptotic distribution of the estimator have been established.