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We study systems of simple point processes that admit stochastic intensities.We represent these point processes as thinnings of Poisson measures and areinterested in a convergence result of such systems. This result states that, ifthe stochastic intensities of the limit point processes are independent of theunderlying Poisson measures, the convergence in distribution in Skorohodtopology of the stochastic intensities implies the same convergence for thepoint processes.

A convergence criterion for systems of point processes from the convergence of their stochastic intensities