MOMENTS OF RANDOMLY STOPPED U-STATISTICS

In this paper we provide sharp bounds on the L-p-norms of randomly sto pped U-statistics. These bounds consist mainly of decoupling inequalit ies designed to reduce the level of dependence between the U-statistic s and the stopping time involved. we apply our results to obtain Wald' s equation for U-statistics, moment convergence theorems and asymptoti c expansions for the moments of randomly stopped U-statistics. The pro ofs are based an decoupling inequalities, symmetrization techniques, t he use of subsequences and induction arguments.