68

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# Stochastic monotonicity and Slepian-type inequalities for infinitely
divisible and stable random vectors

**Gennady Samorodnitsky
**

Murad S. Taqqu

### Abstract:

*We study the relation between stochastic domination of an infinitely
divisible random vector by another infinitely divisible random
vector
and their corresponding Lévy measures. The results are used
to
derive a Slepian-type inequality for a general class of symmetric infinitely
divisible random vectors.
*