  We consider the parameter estimation problem for the non-ergodic fractional
Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a
parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index
$H\in(1/2,1)$. We study the consistency and the asymptotic distributions of the
least squares estimator $\hat{\theta}_t$ of $\theta$ based on the observation
$\{X_s,\ s\in[0,t]\}$ as $t\rightarrow\infty$.
