  We study systems of simple point processes that admit stochastic intensities.
We represent these point processes as thinnings of Poisson measures and are
interested in a convergence result of such systems. This result states that, if
the stochastic intensities of the limit point processes are independent of the
underlying Poisson measures, the convergence in distribution in Skorohod
topology of the stochastic intensities implies the same convergence for the
point processes.
