On moments of integral exponential functionals of additive processes

Abstract For real-valued additive process ( X t ) t ≥ 0 a recursive equation is derived for the entire positive moments of functionals I s , t = ∫ s t exp ( − X u ) d u , 0 ≤ s t ≤ ∞ , 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.