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

doi:10.1007/s11464-019-0801-9

Front. Math. China

2019, Vol. 14

Issue (6) : 1281-1302 https://doi.org/10.1007/s11464-019-0801-9

RESEARCH ARTICLE

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

Guangjun SHEN¹, Qian YU²(

), Yunmeng LI¹

¹. Department of Mathematics, Anhui Normal University, Wuhu 241000, China
². School of Statistics, East China Normal University, Shanghai 200241, China

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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 generaliza- tion of Lévy process.

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

Corresponding Author(s): Qian YU

Issue Date: 07 January 2020

Cite this article:

Guangjun SHEN,Qian YU,Yunmeng LI. Least squares estimator of Ornstein-Uhlenbeck processes driven by fractional Lévy processes with periodic mean[J]. Front. Math. China, 2019, 14(6): 1281-1302.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0801-9
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I6/1281

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