An Exponential Nonuniform Berry–Esseen Bound for the Fractional Ornstein–Uhlenbeck Process

Hui Jiang () and Jingying Zhou ()
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Hui Jiang: Nanjing University of Aeronautics and Astronautics
Jingying Zhou: Nanjing University of Aeronautics and Astronautics

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 1037-1058

Abstract: Abstract In this paper, we study the asymptotic properties of the maximum likelihood estimator of the drift parameter in the fractional Ornstein–Uhlenbeck process. Using the change of measure method and asymptotic analysis technique, we establish an exponential nonuniform Berry–Esseen bound for the maximum likelihood estimator. As an application, the optimal uniform Berry–Esseen bound and Cramér-type moderate deviation are obtained.

Keywords: Berry–Esseen bound; Change of measure method; Cramér-type moderate deviation; Fractional Ornstein–Uhlenbeck process; Maximum likelihood estimator; 60F10; 60G22; 62N02 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01194-w

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