  Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with
parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type
\[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int
_0^t\mu\bigl(X(u)\bigr)\mathrm {d}u.\] In different particular models where
$\sigma(x)=\sigma$ or $\sigma(x)=\sigma x$ and $\mu(x)=\mu$ or $\mu(x)=\mu x$,
we propose a central limit theorem for estimators of $H$ and of $\sigma$ based
on regression methods. Then we give tests of the hypothesis on $\sigma$ for
these models. We also consider functional estimation on $\sigma(\cdot)$ in the
above more general models based in the asymptotic behavior of functionals of
the 2nd-order increments of the fBm.
