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 Limit theorems for non-degenerate U-statistics of continuous semimartingales


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This paper presents the asymptotic theory for non-degenerate U-statistics of high frequency observations of continuous It\^o semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.



Author: Mark Podolskij; Christian Schmidt; Johanna Fasciati Ziegel

Source: https://archive.org/







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