On Distribution of Product of Stable Laws

Abstract

We derive the probability distribution of product of two independent random variables, each distributed according the one-dimensional stable law. We represent the density by its power series and its asymptotic expansions. As Fox's H-functions with a particular choice of parameters well describe the densities of stable laws, we discuss the choice of parameters for Fox's H-function such that it matches the derived densities. As a consequence, we give representations of these particular Fox's H-functions in terms of its power series.