Least squares estimator of Ornstein-Uhlenbeck processes driven by fractional Lévy processes with periodic mean

  • Guangjun Shen
  • Qian YuEmail author
  • Yunmeng Li
Research Article


We deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Lévy process. For this estimator, we obtain consistency and the asymptotic distribution. Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Lévy process, they can be regarded both as a Lévy generalization of fractional Brownian motion and a fractional generalization of Lévy process.


Least squares estimator Ornstein-Uhlenbeck processes fractional Lévy processes asymptotic distribution 


60G18 60G22 65C30 93E24 


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Guangjun Shen was supported by the Distinguished Young Scholars Foundation of Anhui Province (1608085J06), the Top Talent Project of University Discipline (speciality) (Grant No. gxbjZD03), and the National Natural Science Foundation of China (Grant No. 11901005). Qian Yu was supported by the ECNU Academic Innovation Promotion Program for Excellent Doctoral Students (YBNLTS2019-010) and the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management (2018FEM-BCKYB014).


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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsAnhui Normal UniversityWuhuChina
  2. 2.School of StatisticsEast China Normal UniversityShanghaiChina

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