An estimate about multiple stochastic integrals with respect to a normalized empirical measure

@inproceedings{Major2005AnEA,
title={An estimate about multiple stochastic integrals with respect to a normalized empirical measure},
author={Peter 4 Major},
year={2005}
}

where prime means that the diagonals are omitted from the domain of integration. A good bound is given on the probability P (|Jn,k(f)| > x) for all x > 0 which is similar to the estimate in the analogous problem we obtain by considering the Gaussian (multiple) Wiener–Itô integral of the function f . The proof is based on an adaptation of some methods of the theory of Wiener–Itô integrals. In particular, a sort of diagram formula is proved for the random integrals Jn,k(f) together with some of… CONTINUE READING

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