<t>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)\...

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