On moments of integral exponential functionals of additive processes

Abstract: For real-valued additive process $(X_t)_{t\geq 0}$ a recursive equation is derived for the entire positive moments of functionals $$I_{s,t}= \int _s^t\exp(-X_u)du, \quad 0\leq s<t\leq\infty, $$ in case the Laplace exponent of $X_t$ exists for positive values of the parameter. From the equation emergesan easy-to-apply sufficient condition for the finiteness of the moments. As an application we study first hitprocesses of diffusions.