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**Background**


I've been reading this article and it keeps referring to "Grigelionis processes", which apparently generalize Levy processes. However the paper does not define these object clearly and assumes the reader be familiar with the general definition. 




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**Question:**
So what is the precise definition of a ***Grigelionis Process*** and what does it represent intuitively?



Definition: Grigelionis Process?
A Grigelionis process is a special semimartingale with *absolutely continuous* integral characteristics (in time). This is insofar a generalization of a Lévy process, as Lévy processes can be characterized as special semimartingales with *linear* integral characteristics (in time).


A nice starting point seems to be [Jan Kallsen's PhD thesis](http://www.math.uni-kiel.de/numerik/kallsen/personen/kallsen/pub/diss.ps), section 2.3.


