An Asymptotic Evaluation of the Tail of a Multiple Symmetric $\alpha$- Stable Integral

Abstract

We expand a multiple symmetric $\alpha$-stable integral $\int \cdots \int f(t_1, \ldots, t_n) dM(t_1) \ldots dM(t_n)$ into a LePage type multiple series of transformed arrival times of a Poisson process. An exact evaluation of the limit of appropriately normalized tail distribution results from this representation.