  In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property
for the statistical model given by the observation of local means of a
diffusion process $X$. Our data are given by $ \int_0^1 X_{\frac{s+i}{n}} \dd
\mu (s)$ for $i=0,...,n-1$ and the unknown parameter appears in the diffusion
coefficient of the process $X$ only. Although the data are nor Markovian
neither Gaussian we can write down, with help of Malliavin calculus, an
explicit expression for the log-likelihood of the model, and then study the
asymptotic expansion. We actually find that the asymptotic information of this
model is the same one as for a usual discrete sampling of $X$.
