Summary
We give a necessary and sufficient condition for the convergence in law
of simple point processes on ℝ+, for Skorokhod topology, in terms of their predictable compensatorsA n andA. The assumptions are thatA t(ω) is continuous in (ω,t) and meets some mild integrability condition. The condition is thatA n converges “weakly” toA in a suitable sense.
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Jacod, J. Sur la convergence des processus ponctuels. Probab. Th. Rel. Fields 76, 573–586 (1987). https://doi.org/10.1007/BF00960075
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DOI: https://doi.org/10.1007/BF00960075