On moments of integral exponential functionals of additive processes.

For real-valued additive process $(X_t)_{tgeq 0}$ % i.e., a process with independent increments a recursive equation is derived for the entire positive moments of functionals

I_{s,t}= int _s^texp(-X_u)du, quad 0leq s

in case the Laplace exponent of $X_t$ exists for positive values of the parameter.From the equation emerges an easy-to-apply sufficient condition for the finiteness of the moments. As an application we study first hit processes of diffusions.