Hi everyone,
I've had this frustating, silly problem for a while now. I've looked at the problem for a loooong time now, which may be one of the reasons I can't see the solution. I am trying to calculate the characteristic function of a basic jump process.
The theory is presented in the attached pictures and is taken from a paper by Eckner.
The problem is that I don't know how to use the interpretation of $\gamma$, like in the appendice A.2. of the paper, when calculating the characteristic function instead of moment generating function . I mean that I don't know how the interpretation of $\gamma$ changes the way I calculate? I tried looking for the solution from the paper by Lord& Kahl that is mentioned (http://www2.math.uni-wuppertal.de/~kahl/publications/whytherotationcountalgorithmworks.pdf) but it still remains a mystery to me, how I should adjust the known closed-form solution of moment generating function in order to find the characteristic function. I think I do understand why the interpretation is made and, but I am not quite sure though...
I would be truly glad if someone would be so kind to explain to explain the practical meaning of the interpretation!