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

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 \(H \in (0,{1 \over 2})\) $$H\in (0,\frac{1}{2})$$ . 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.