## JMI2010A-2 On the exponential moments of additive processes with the structure of semimartingales (pp.13-20)

Author(s)： Tsukasa Fujiwara

J. Math-for-Ind. **2A** (2010) 13-20.

- File： JMI2010A-2.pdf (125KB)

Abstract

In this paper, the exponential moments of $\mathbb{R}$-valued additive processes with the strucure of semimartingales, which are regarded as the Laplace transforms of the laws of these additive processes, will be explicitly represented by their characteristics. Note that the additive processes investigated here will not necessarily be assumed to be stochastically continuous. To prove the result, a criterion proposed in [5], which is described by the modified Laplace cumulant, will be applied.

Keyword(s). additive process, semimartingale, exponential moment, Laplace cumulant, modifiedLaplace cumulant