Parameters estimation for ornstein-uhlenbeck processes with time periodic modulated drift

Abstract

Abstract This work mainly delves into the parameter estimation problem concerning Ornstein-Uhlenbeck processes with time-periodic modulated drift based on continuous observations. A least squares estimator is constructed by minimizing a contrast function. It is demonstrated that as the number of observed periods approaches infinity, the least squares estimator exhibits asymptotic unbiasedness, strong consistency, and asymptotic normality. The important technique in the asymptotic study relies on the central limit theorem for multiple Wiener integrals. Finally, numerical simulations of the least squares estimator are presented.