Tail behaviour of multiple random integrals and U-statistics
Abstract
This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito integrals with respect to a white noise. It also contains good estimates about the supremum of appropriate classes of such integrals or U-statistics. The proof of most results is omitted, I have concentrated on the explanation of their content and the picture behind them. I also tried to explain the reason for the investigation of such questions. My goal was to yield such a presentation of the results which a non-expert also can understand, and not only on a formal level.
Cite
@article{arxiv.math/0512238,
title = {Tail behaviour of multiple random integrals and U-statistics},
author = {Peter Major},
journal= {arXiv preprint arXiv:math/0512238},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/154957805100000186 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)