On the Exponential Moments of Additive Processes

Abstract

. A theorem on the exponential moments of general R -valued additive processes will be established. A condition that implies the integrability of the exponential of additive processes will be proposed and furthermore the representation of their exponential moments by their characteristics will be shown. In the previous paper [1], the same problem as above has been investigated in the case when the underlying additive processes have the structure of semimartingales. In this paper, another proof for this case will be presented. It will be more inherent and simpler than the previous one. Moreover, the result will be generalized to the case when the underlying additive processes do not necessarily have the structure of semimartingales.