## The Annals of Applied Probability

### Limit theorems for nondegenerate U-statistics of continuous semimartingales

#### Abstract

This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous Itô 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.

#### Article information

Source
Ann. Appl. Probab., Volume 24, Number 6 (2014), 2491-2526.

Dates
First available in Project Euclid: 26 August 2014

https://projecteuclid.org/euclid.aoap/1409058038

Digital Object Identifier
doi:10.1214/13-AAP983

Mathematical Reviews number (MathSciNet)
MR3262509

Zentralblatt MATH identifier
1308.60051

#### Citation

Podolskij, Mark; Schmidt, Christian; Ziegel, Johanna F. Limit theorems for nondegenerate U -statistics of continuous semimartingales. Ann. Appl. Probab. 24 (2014), no. 6, 2491--2526. doi:10.1214/13-AAP983. https://projecteuclid.org/euclid.aoap/1409058038

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