Asymptotic behaviour of exponential functionals of Lévy processes with applications to random processes in random environment

Sandra Palau, Juan Carlos Pardo, Charline Smadi

Let $\xi =({\xi }_t,t\ge 0)$ be a real-valued Lévy process and define its associated exponential functional as follows \[ I_t(ξ):=\int_0^t \exp\{-ξ_s\}{\rm d} s, \qquad t\ge 0. \] Motivat…