Quantitative and stable limits of high-frequency statistics of Lévy processes: a Stein's method approach
arxiv(2023)
摘要
We establish inequalities for assessing the distance between the distribution
of errors of partially observed high-frequency statistics of multidimensional
Lévy 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.
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