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Asymptotic Behaviour of the Trajectory Fitting Estimator for Reflected Ornstein–Uhlenbeck Processes

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  • Qingpei Zang

    (Huaiyin Normal University)

  • Lixin Zhang

    (Zhejiang University)

Abstract

The Ornstein–Uhlenbeck process with reflection, which has been the subject of an enormous body of literature, both theoretical and applied, is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. In this work, we are mainly concerned with the study of the asymptotic behavior of the trajectory fitting estimator for nonergodic reflected Ornstein–Uhlenbeck processes, including strong consistency and asymptotic distribution. Moreover, we also prove that this kind of estimator for ergodic reflected Ornstein–Uhlenbeck processes does not possess the property of strong consistency.

Suggested Citation

  • Qingpei Zang & Lixin Zhang, 2019. "Asymptotic Behaviour of the Trajectory Fitting Estimator for Reflected Ornstein–Uhlenbeck Processes," Journal of Theoretical Probability, Springer, vol. 32(1), pages 183-201, March.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:1:d:10.1007_s10959-017-0796-7
    DOI: 10.1007/s10959-017-0796-7
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    References listed on IDEAS

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    Cited by:

    1. Hui Jiang & Jingying Zhou, 2023. "An Exponential Nonuniform Berry–Esseen Bound for the Fractional Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1037-1058, June.
    2. Hui Jiang & Yajuan Pan & Xiao Wei, 2024. "Self-Normalized Cramér-Type Moderate Deviations for Explosive Vasicek Model," Journal of Theoretical Probability, Springer, vol. 37(1), pages 228-250, March.
    3. Hui Jiang & Qingshan Yang, 2022. "Moderate Deviations for Drift Parameter Estimations in Reflected Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1262-1283, June.

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