Revisiting integral functionals of geometric Brownian motion

On distributions of exponential functionals of the processes with independent increments

“…Theorem 1. Under the assumptions (3), (4) and (5), the infinitesimal generator (A V s ) 0≤s<t of the Markov process V is given by (12). In addition, for 0 ≤ s ≤ t and f ∈ C…”

“…Some rather complicated formulas concerning p t were given in [17] and in [13], formula 1.10.4, p. 264. Recently, in [12], based on the derived differential equation for the distribution function, we obtained the Laplace transform for the density of the exponential integral functional of a Brownian motion with drift, Proof. We take the equation (34) Proof.…”