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# The empirical process of some
long-range dependent sequences

**Herold Dehling
**

Murad S. Taqqu

### Abstract:

*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.