Least squares estimator for Ornstein–Uhlenbeck processes driven by fractional Lévy processes from discrete observations
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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 \(t_i=i/n,\)\(i=1,\ldots ,n\) 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.
KeywordsOrnstein–Uhlenbeck processes Fractional Lévy processes Least squares estimator Asymptotic distribution
Mathematics Subject Classification60G18 65C30 93E24
The authors are very grateful to the anonymous referee and the editor for their insightful and valuable comments, which have improved the presentation of the paper. Research supported by the Distinguished Young Scholars Foundation of Anhui Province (1608085J06), the Top Talent Project of University Discipline (Speciality) (gxbjZD03), the National Natural Science Foundation of China (11271020).
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