  We establish inequalities for assessing the distance between the distribution
of errors of partially observed high-frequency statistics of multidimensional
L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we
provide a general result guaranteeing stable functional convergence. Our
arguments rely on a suitable adaptation of the Stein's method perspective to
the context of mixed Gaussian distributions, specifically tailored to the
framework of high-frequency statistics.
