LAN property for some fractional type Brownian motion

We study asymptotic expansion of the likelihood of a certain class of Gaussian processes characterized by their spectral density $f_{\theta }$. We consider the case where $f_\theta\PAR{x} \sim_{x\to 0} \ABS{x}^{-\al(\theta)}L_\theta(x)$with$L_\theta$ a slowly varying function and $\text{al}\text{PAR}\theta \in (-\mathrm{\infty },1)$. We prove LAN property for these models which include in particular fractional Brownian motion %$B^\alpha_t,: \alpha \geq 1/2$ or ARFIMA processes.