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

LAN property for some fractional type Brownian motion