Tail behavior of random products and stochastic exponentials

Serge Cohen (1) , Thomas Mikosch (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Laboratory of Actuarial Mathematics

In 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.

Serge Cohen, Thomas Mikosch. Tail behavior of random products and stochastic exponentials. Stochastic Processes and their Applications, 2008, 118, pp.333-345. ⟨10.1016/j.spa.2007.05.003⟩. ⟨hal-00625304⟩