Multiple stable integrals of Banach-valued functions

Gennady Samorodnitsky
Murad S. Taqqu


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.