Abstract: 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. Th...

Multiple Stratonovich integrals (MSI) with respect to the Wiener process and the Brownian bridge are defined for a class of kernels having k-th order t-traces which are, in general different from the traces investigated in earlier work. Asymptotic distributions of V-statistics are derived and the limiting distribution expressed in terms of appropriate MSI. Another application yields an alternat...