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<H1>L&#233;vy measures of infinitely divisible random vectors and Slepian
inequalities</H1>
<P><STRONG>Gennady Samorodnitsky
<BR> Murad S. Taqqu</STRONG><P>
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<H3>Abstract:</H3>
<EM>We study Slepian inequalities for general non-Gaussian infinitely divisible
random vectors. Conditions for such inequalities are expressed in terms of
the corresponding L&#233;vy measures of these vectors. These conditions are
shown to be nearly  best possible, and for a large subfamily of 
these conditions are necessary and sufficient for Slepian inequalities. As
an application we consider  Ornstein-Uhlenbeck processes and a family of
 introduced by Brown and Rinott.
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