  We consider a stochastic differential equation with additive fractional noise
with Hurst parameter $H>1/2$, and a non-linear drift depending on an unknown
parameter. We show the Local Asymptotic Normality property (LAN) of this
parametric model with rate $\sqrt{\tau}$ as $\tau\rightarrow \infty$, when the
solution is observed continuously on the time interval $[0,\tau]$. The proof
uses ergodic properties of the equation and a Girsanov-type transform. We
analyse the particular case of the fractional Ornstein-Uhlenbeck process and
show that the Maximum Likelihood Estimator is asymptotically efficient in the
sense of the Minimax Theorem.
