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.