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The functional law of the iterated logarithm for 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 . Consider the two-parameter empirical process for , where G is any measurable function. The Functional Law of the Iterated Logarithm as well as a Strong Invariance Principle are obtained for . Applications to U-statistics and von Mises statistics are given.