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 $f_θ$. We consider the case where $f_θ\PAR{x} \sim_{x\to 0} \ABS{x}^{-\al(θ)}L_θ(x)$ with $L_θ$ a slowly varying function and $\al\PARθ\in (-\infty,1)$. We prove LAN property for these models which include in particular fractional Brownian motion %$B^α_t,\: α\geq 1/2$ or ARFIMA processes.

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