The empirical process of some long-range dependent sequences

Herold Dehling
Murad S. Taqqu


Let be a stationary, mean-zero Gaussian process with covariances satisfying and where D is small and L is slowly varying at infinity. Consider the two-parameter empirical process for , where G is any measurable function. Non-central limit theorems are obtained for and they are used to derive the asymptotic behavior of some suitably normalized von Mises statistics and U-statistics based on the 's. The limiting processes are structurally different from those encountered in the i.i.d. case.