Drift parameter identification for the Ornstein-Uhlenbeck process driven by Ornstein-Uhlenbeck with small General Gaussian noise

We address the drift parameter identification problem for an Ornstein-Uhlenbeck process driven by an Ornstein-Uhlenbeck dynamic with small general Gaussian noise. The general Gaussian noise includes several processes such as fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, and generalized sub-fractional Brownian motion, among others. By applying the least squares method, we obtain a parameter estimator for this model, whose convergence and a central-type limit theorem are established under certain conditions.