# Inhomogeneous Compound Poisson process

I need to use a compound Poisson process with time-varying jump intensity. Mathematica has the function of compound Poisson process as well as inhomogeneous Poisson process, but no combination of these two. Is it possible to create such a process? In addition, how to create contemporaneous compound processes with different jump distributions, that is two jump processes controlled by the same Poisson counter. Thanks in advance!

• I am not sufficiently familiar with these distributions to give you a concrete answer, but if these distributions can be constructed from more simpler ones, you should have a look at MixtureDistribution, ParameterMixtureDistribution, and TransformedDistribution. Even more ways to modify distributions can be found here. – Henrik Schumacher Sep 14 '18 at 6:35