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

Chiara Amorino; Arturo Jaramillo; Mark Podolskij

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arXiv · 2302.05885

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

Chiara Amorino·Arturo Jaramillo·Mark Podolskij

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Abstract

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.

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Chiara Amorino, Arturo Jaramillo, Mark Podolskij. 2023-02-12. Quantitative and stable limits of high-frequency statistics of L\'evy processes: a Stein's method approach. https://arxiv.org/abs/2302.05885

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