Least squares estimator of fractional Ornstein-Uhlenbeck processes with periodic mean

We first study the drift parameter estimation of the fractional Ornstein-Uhlenbeck process (fOU) with periodic mean for every 12<H<1. More precisely, we extend the consistency proved in Dehling et al. (2016) for 12<H<34 to the strong consistency for any 12<H<1 on the one hand, and on the other, we also discuss the asymptotic normality given in Dehling et al. (2016). In the second main part of the paper, we study the strong consistency and the asymptotic normality of the fOU of the second kind with periodic mean for any 12<H<1.