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# How do conditional moments of stable vectors
depend on the spectral measure?

**Renata Cioczek-Georges
**

Murad S. Taqqu

### Abstract:

*Let be an -stable random vector with , not necessarily symmetric. Its distribution is characterized by
a finite measure on the unit circle called the spectral
measure. It is known that if satisfies some
integrability condition then the conditional moment
can exist for some values of ***p** greater than . This paper
provides a sufficient condition on
for the existence of the conditional
moment involving the * maximal* range of possible **p**'s,
namely .
*
*