Tail behaviour of multiple random integrals and \(U\)-statistics. (English) Zbl 1189.60061

Summary: 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.


60F10 Large deviations
60G50 Sums of independent random variables; random walks
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