Invariance principles for U-statistics and von Mises functionals (Q1121612)

Using a new type of stochastic integral with respect to Kiefer processes of a certain covariance structure it is shown that a weak invariance principle for degenerate U-statistics holds whenever the underlying observations are uniformly mixing in both directions of time or absolutely regular. Certain rates in the mixing condition and some moment conditions are needed. The paper also gives applications when the kernel is of degree 2.