I would like to integrate z^2 over a Levy measure and simulate the results. How best shall I go about it?

(i) Are you sure that your Levy measure ensures that the second moment of the process is finite? Otherwise it will just be infinite (I assume you want to integrate over the whole real line).(ii) Does your Levy measure have a density?

i would love to try and solve it for you. please do give me more details as to the exact form of the Levy measure you are talking about.

Indeed $$ \int_{\mathbb R}min(1,x^2)nu(dx)<\infty$$. I happen to have got a way of approximating the integral. Protter's book says that\begin{eqnarray}\mathbb E [\int_A f(z)N(t,dz)]&=&t\int_Af(z)\nu(dz)\\\mathbb E [(\int_A f(z)N(t,dz)-t\int_Af(z)\nu(dz))^2]&=&t\int_Af(z)^2\nu(dz)\end{eqnarray}The above detail is written in Tex; I hope you are familiar with it.However, I do not have a density for the process seeing that I am modeling a generalcase. I hope to include a particular case in my research and may start with uniformlydistributed jump amplitudes....If you have any suggestions kindly inform me.