Open Access
2005 Tail behaviour of multiple random integrals and U-statistics
Péter Major
Probab. Surveys 2: 448-505 (2005). DOI: 10.1214/154957805100000186


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–Itô 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.


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Péter Major. "Tail behaviour of multiple random integrals and U-statistics." Probab. Surveys 2 448 - 505, 2005.


Published: 2005
First available in Project Euclid: 12 December 2005

zbMATH: 1189.60061
MathSciNet: MR2203678
Digital Object Identifier: 10.1214/154957805100000186

Primary: 60F10
Secondary: 60G50

Keywords: (degenerate) U-statistics , decoupling method , diagram formula , L_{p}-dense classes of functions , large-deviation type estimates , multiple Wiener–Itô integrals , symmetrization

Rights: Copyright © 2005 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.2 • 2005
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