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<H1>The functional law of the iterated logarithm for the empirical
process of some long-range dependent sequences</H1>
<P><STRONG>Herold Dehling
<BR> Murad S. Taqqu</STRONG><P>
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<H3>Abstract:</H3>
<EM>Let  <IMG  ALIGN=MIDDLE ALT="" SRC="img1.gif">  be a stationary, mean-zero 
Gaussian process with covariances  <IMG  ALIGN=MIDDLE ALT="" SRC="img2.gif">
 <IMG  ALIGN=MIDDLE ALT="" SRC="img3.gif">  satisfying  <IMG  ALIGN=MIDDLE ALT="" SRC="img4.gif">  and  <IMG  ALIGN=MIDDLE ALT="" SRC="img5.gif">.  Consider the two-parameter empirical process
 for  <IMG  ALIGN=MIDDLE ALT="" SRC="img6.gif">,
where <b>G</b>  is any measurable function. The Functional Law of the Iterated 
Logarithm as well as a Strong Invariance Principle are obtained for  <IMG  ALIGN=MIDDLE ALT="" SRC="img7.gif">.
  Applications to U-statistics and von Mises statistics are given.
</EM><P>


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