Before revision:  When X is a semi-martingale with absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of I\_t, and also the sufficient conditions of finiteness of the Mellin transform {\bf E}( I \_t^{\alpha \alpha\in\mathbb{R} . We give a recurrent integral equations for this Mellin transform .
After revision:  When X is a semi-martingale with absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of I\_t, and also the sufficient conditions of finiteness of the Mellin transform {\bf E}( I \_t^{\alpha \alpha\in\mathbb{R} , of the integral functional I_t .