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Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with \(H \in (0,{1 \over 2})\)

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Abstract

In this paper, we study the asymptotic properties for estimators of two parameters in the drift function in the ergodic fractional Ornstein-Uhlenbeck process with Hurst index \(H \in (0,{1 \over 2})\). The Cramér-type moderate deviations, as well as the moderation deviations with explicit rate function can be obtained. The main methods consist of the deviation inequalities and Cramér-type moderate deviations for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.

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Authors and Affiliations

  1. School of Mathematics, Nan**g University of Aeronautics and Astronautics, Nan**g, 211106, China

    Hui Jiang

  2. MOE Key Laboratory of Applied Statistics, School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China

    Qing-shan Yang

Authors
  1. Hui Jiang
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  2. Qing-shan Yang
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Corresponding author

Correspondence to Qing-shan Yang.

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The authors declare no conflict of interest.

Additional information

Hui JIANG is supported by the Natural Science Foundation of Jiangsu Province (No.BK20231435) and Fundamental Research Funds for the Central Universities (No.NS2022069). Qing-shan YANG is supported by National Natural Science Foundation of China (Grant NO.11401090, 11971097, 11971098).

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Jiang, H., Yang, Qs. Moderate Deviations for the Parameter Estimation in the Fractional Ornstein-Uhlenbeck Process with \(H \in (0,{1 \over 2})\). Acta Math. Appl. Sin. Engl. Ser. (2024). https://doi.org/10.1007/s10255-024-1083-x

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  • DOI: https://doi.org/10.1007/s10255-024-1083-x

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