Parametric estimation for sub-fractional Ornstein–Uhlenbeck process

We consider the parameter estimation problem for the sub-fractional Ornstein–Uhlenbeck process defined as X0=0,dXt=θXtdt+dStH, t⩾0,t⩾0, with parameter θ>0θ>0, where SH is a sub-fractional Brownian motion with index H>12. We study the consistency and the asymptotic distribution of the least squares estimator θ^t of θθ based on the observation {Xs,s∈[0,t]}{Xs,s∈[0,t]} as t→∞t→∞.