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We establish inequalities for assessing the distance between the distributionof errors of partially observed high-frequency statistics of multidimensionalL\'evy processes and that of a mixed Gaussian random variable. Furthermore, weprovide a general result guaranteeing stable functional convergence. Ourarguments rely on a suitable adaptation of the Stein's method perspective tothe context of mixed Gaussian distributions, specifically tailored to theframework of high-frequency statistics.

Quantitative and stable limits of high-frequency statistics of L\'evy processes: a Stein's method approach