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Moderate Deviations for Drift Parameter Estimations in Reflected Ornstein–Uhlenbeck Process

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  • Hui Jiang

    (Nanjing University of Aeronautics and Astronautics)

  • Qingshan Yang

    (Northeast Normal University)

Abstract

In this paper, we study the asymptotic properties of drift parameter estimations in reflected Ornstein–Uhlenbeck process, and establish their moderate deviations in both cases with one-sided barrier and two-sided barriers. The main methods consist of regenerative process techniques and the strong Markov property, as well as moderate deviations for martingales.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-021-01096-3
    DOI: 10.1007/s10959-021-01096-3
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    References listed on IDEAS

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    1. Es-Sebaiy, Khalifa & Viens, Frederi G., 2019. "Optimal rates for parameter estimation of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3018-3054.
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    3. Yaozhong Hu & Chihoon Lee & Myung Lee & Jian Song, 2015. "Parameter estimation for reflected Ornstein–Uhlenbeck processes with discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 279-291, October.
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    5. Michel Mandjes & Peter Spreij, 2017. "A note on the central limit theorem for the idleness process in a one-sided reflected Ornstein–Uhlenbeck model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(3), pages 225-235, August.
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