EAN: 9783642376160

ON THE ESTIMATION OF MULTIPLE RANDOM INTEGRALS ...

This work starts with the study of those limit theorems in probability theory for which
classical methods do not work. In many cases some form of linearization can help to solve the
problem  because the linearized version is simpler. But in order to apply such a method we have
to show that the linearization causes a negligible error. The estimation of this error leads to
some important large deviation type problems  and the main subject of this work is their
investigation. We provide sharp estimates of the tail distribution of multiple integrals with
respect to a normalized empirical measure and so-called degenerate U-statistics and also of the
supremum of appropriate classes of such quantities. The proofs apply a number of useful
techniques of modern probability that enable us to investigate the non-linear functionals of
independent random variables. This lecture note yields insights into these methods  and may
also be useful for those who only want some new tools to help them prove limit theorems when
standard methods are not a viable option.

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