For a Lévy process ξ=(ξt) t⩾ 0 drifting to−∞, we define the so‐called exponential functional
as follows: I ξ=∫ 0∞ e ξ tdt. Under mild conditions on ξ, we show that the following …

Let $\xi=(\xi_t, t\ge 0) $ be a real-valued L\'evy process and define its associated exponential
functional as follows\[I_t (\xi):=\int_0^ t\exp\{-\xi_s\}{\rm d} s,\qquad t\ge 0.\] Motivated by …

In 18, under mild conditions, a Wiener-Hopf type factorization is derived for the exponential
functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a …

Exponential functionals of Brownian motion have been extensively studied in financial and
insurance mathematics due to their broad applications, for example, in the pricing of Asian …

Exponential functionals of Lévy processes appear as stationary distributions of generalized
Ornstein–Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of …

We investigate ergodic properties of the solution of the SDE d V t= V t− d U t+ d L t, where (U,
L) is a bivariate Lévy process. This class of processes includes the generalized Ornstein …

In this work, we consider moments of exponential functionals of Lévy processes on a
deterministic horizon. We derive two convolutional identities regarding these moments. The …

We find necessary and sufficient conditions for almost sure finiteness of integral functionals
of spectrally positive Lévy processes under conditional probabilities. Via Lamperti-type …

We study the exponential functional $\int_0^\infty e^{-\xi_ {s-}}\, d\eta_s $ of two one-
dimensional independent L\'evy processes $\xi $ and $\eta $, where $\eta $ is a …

In this paper, we study the exponential functionals of the processes X with independent
increments, namely, I_t=\int_0^t\exp{-X_s\}\,ds,\t≧0, and also I_∞=\int_0^∞\exp{-X_s\}\,ds …