  In this paper we propose the use of $\phi$-divergences as test statistics to
verify simple hypotheses about a one-dimensional parametric diffusion process
$\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete
observations $\{X_{t_i}, i=0, ..., n\}$ with $t_i = i\Delta_n$, $i=0, 1, >...,
n$, under the asymptotic scheme $\Delta_n\to0$, $n\Delta_n\to\infty$ and
$n\Delta_n^2\to 0$. The class of $\phi$-divergences is wide and includes
several special members like Kullback-Leibler, R\'enyi, power and
$\alpha$-divergences. We derive the asymptotic distribution of the test
statistics based on $\phi$-divergences. The limiting law takes different forms
depending on the regularity of $\phi$. These convergence differ from the
classical results for independent and identically distributed random variables.
Numerical analysis is used to show the small sample properties of the test
statistics in terms of estimated level and power of the test.
