  We want to compute the cumulative distribution function of a one-dimensional
Poisson stochastic integral $I(\krnl) = \displaystyle \int_0^T \krnl(s) N(ds)$,
where $N$ is a Poisson random measure with control measure $n$ and $\krnl$ is a
suitable kernel function. We do so by combining a Kolmogorov-Feller equation
with a finite-difference scheme. We provide the rate of convergence of our
numerical scheme and illustrate our method on a number of examples. The
software used to implement the procedure is available on demand and we
demonstrate its use in the paper.
