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# Multiple stable integrals of Banach-valued functions

**Gennady Samorodnitsky
**

Murad S. Taqqu

### Abstract:

*This paper extends results of
Samorodnitsky and Szulga to
separable Banach
spaces ***S** of Rademacher-type . Let
be an integral
of order **n** with respect to a symmetric -stable random measure **M**,
,
with a Radon control measure **m**, and let
be a symmetric deterministic function
vanishing on the diagonals.
If the norm of **f** satisfies a given integrability condition, then
is well defined and the probability that the
norm of exceeds is asymptotic to a
constant dependind on ,**n** and **f** times
as . In the case **n=2** and , the
integrability condition reduces to the known necessary and sufficient
condition of Rosinski and Woyczynski []
and Kwapien and Woyczynski []. The
paper concludes with some applications.