Tail behavior of random products and stochastic exponentials

In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance αα-stable Lévy motion. We show that the solution is regularly varying with index αα. An important step in the proof is the study of a Poisson number of products of independent random variables with regularly varying tail. The study of these products merits its own interest because it involves interesting saddle-point approximation techniques.