= Poisson stochastic integral with finite intensity
{c}
{title2=$\int_E f(z)\,N(dz)$}
For a <Poisson random measure> on $E$ with finite intensity $\nu(E)$, its integral of a finite-valued measurable mark function is the finite sum of the marks at its random atoms. Its <characteristic function> is $\mathbb E\exp(iu\int f\,dN)=\exp(\int(e^{iuf}-1)\,d\nu)$. On a time-mark space with intensity $ds\,\nu(dz)$ and finite mark intensity, restriction to each bounded time interval has finite intensity and defines a <Compound Poisson process>. Zero-valued marks do not affect the integral and need not appear in its <Lévy measure>.
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