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Least squares estimator for Ornstein–Uhlenbeck processes driven by small fractional Lévy noises

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  • Qingbo Wang
  • Guangjun Shen
  • Zhenlong Gao

Abstract

In this paper, we study the problem of parameter estimation for the Ornstein–Uhlenbeck processes{dXt=θXtdt+dYt dYt=Ytdt+εdLtd driven by Ornstein–Uhlenbeck processes with small fractional Lévy noises and Yt can be observed, based on discrete high frequency observations at regularly spaced time points {tk=kn, k=1,…,n} on [0,1]. We obtain the consistency as well as the asymptotic behavior of the least squares estimator of the unknown parameter θ when ε→0 and n→∞ simultaneously.

Suggested Citation

  • Qingbo Wang & Guangjun Shen & Zhenlong Gao, 2021. "Least squares estimator for Ornstein–Uhlenbeck processes driven by small fractional Lévy noises," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(8), pages 1838-1855, April.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:8:p:1838-1855
    DOI: 10.1080/03610926.2019.1653923
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    Cited by:

    1. Xuekang Zhang & Huisheng Shu & Haoran Yi, 2023. "Parameter Estimation for Ornstein–Uhlenbeck Driven by Ornstein–Uhlenbeck Processes with Small Lévy Noises," Journal of Theoretical Probability, Springer, vol. 36(1), pages 78-98, March.

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