The non-semimartingale nature of the fBm makes the statistical analysis of related continuous-time processes complicated. In this talk, taking up the fBm with fitted trend and the fractional O-U process, I discuss how to compute the distributions of the LSE and MLE for the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). We also derive the asymptotic distribution of the MLE as the time span M becomes large. We further conduct the unit root test under the error process following the fBm.