On U- and V-statistics for discontinuous Ito semimartingales
Probability
2015-05-25 v1
Abstract
In this paper we examine the asymptotic theory for U-statistics and V-statistics of discontinuous Ito semimartingales that are observed at high frequency. For different types of kernel functions we show laws of large numbers and associated stable central limit theorems. In most of the cases the limiting process will be conditionally centered Gaussian. The structure of the kernel function determines whether the jump and/or the continuous part of the semimartingale contribute to the limit.
Keywords
Cite
@article{arxiv.1505.06119,
title = {On U- and V-statistics for discontinuous Ito semimartingales},
author = {Mark Podolskij and Christian Schmidt and Mathias Vetter},
journal= {arXiv preprint arXiv:1505.06119},
year = {2015}
}