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On mixed Poisson processes and martingales. (English) Zbl 1021.60039
Summary: O. Lundberg’s martingale characterization of mixed Poisson processes with finite mean value within birth processes is extended to mixed Poisson processes with arbitrary mixing distributions within the class of general point processes. Some applications of this result are also discussed.

MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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