Let (Xt) be a diffusion on the interval (l,r) and Δn
a sequence of positive numbers tending to zero. We define Ji as the integral
between iΔn and (i + 1)Δn of Xs.
We give an approximation of the law of (J0,...,Jn-1)
by means of a Euler scheme expansion for the process (Ji).
In some special cases, an approximation by an
explicit Gaussian ARMA(1,1) process is obtained.
When Δn = n-1 we deduce from this expansion estimators
of the diffusion coefficient of X based on (Ji). These estimators
are shown to be asymptotically mixed normal as n tends to infinity.