Bernstein-gamma functions and exponential functionals of Levy Processes

Pierre Patie, Mladen Savov

We study the equation $M_{\Psi }(z+1)=\frac{-z}{\Psi (-z)}{M}_{\Psi }(z),M_{\Psi }(1)=1$ defined on a subset of the imaginary line and where $\Psi$ is a negative definite functions. Using the Wiener-Hopf me…