Parametric estimation for sub-fractional Ornstein–Uhlenbeck process

We consider the parameter estimation problem for the sub-fractional Ornstein–Uhlenbeck process defined as X 0 = 0 , dX t = θ X t dt + dS t H , t ⩾ 0 , with parameter θ > 0 , where SH is a sub-fractional Brownian motion with index H > 1 2 . We study the consistency and the asymptotic distribution of the least squares estimator θ ^ t of θ based on the observation { X s , s ∈ [ 0 , t ] } as t → ∞ .