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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241000, China

    Guangjun Shen & Yunmeng Li

  2. School of Statistics, East China Normal University, Shanghai, 200241, China

    Qian Yu

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  1. Guangjun Shen
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  2. Qian Yu
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  3. Yunmeng Li
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Correspondence to Qian Yu.

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Shen, G., Yu, Q. & Li, Y. Least squares estimator of Ornstein-Uhlenbeck processes driven by fractional Lévy processes with periodic mean. Front. Math. China 14, 1281–1302 (2019). https://doi.org/10.1007/s11464-019-0801-9

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  • DOI: https://doi.org/10.1007/s11464-019-0801-9

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