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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Héctor Araya,
  • Francisco Plaza-Vega,
  • Eloy Alvarado

摘要

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.