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The paper shows that the distribution of the normalized minimum contrast estimator of the drift parameter in the fractional Ornstein-Uhlenbeck process observed over [0, T] converges to the standard normal distribution with an uniform error rate of the order O(T−1/2) for the case H &gt; 1/2 where H is the Hurst exponent of the fractional Brownian motion driving the Ornstein-Uhlenbeck process. Then based on discrete observations, it introduces several approximate minimum contrast estimators and studies their rate of of weak convergence to normal distribution.

Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling