Tail behavior of random products and stochastic exponentials

International audienceIn this paper we study the dsitributional tail behavior of the solution to a linear sde driven by infinite variance $\alpha$-stable Lévy motion. We show that the solution is regularly varying with index $\alpha$. An important step in the proof is the study of a Poisson number of products of independent random variables with regular tail. The study of these products deserves its own interest because it involves interesting saddle-point approximation techniques