@article{EJP430,
author = {Peter Major},
title = {On a Multivariate Version of Bernstein's Inequality},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {12},
year = {2007},
keywords = {Bernstein inequality, (degenerate) U-statistics, Wiener--It^o integrals, diagram formula, moment estimates},
abstract = {We prove such a multivariate version of Bernstein's inequality about the tail distribution of degenerate $U$-statistics which is an improvement of some former results. This estimate will be compared with an analogous bound about the tail distribution of multiple Wiener-Ito integrals. Their comparison shows that our estimate is sharp. The proof is based on good estimates about high moments of degenerate $U$-statistics. They are obtained by means of a diagram formula which enables us to express the product of degenerate $U$-statistics as the sum of such expressions.},
pages = {no. 34, 966-988},
issn = {1083-6489},
doi = {10.1214/EJP.v12-430},
url = {http://ejp.ejpecp.org/article/view/430}}