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In: Mathematica Slovaca, vol. 69, no. 2
Demetrios P. Lyberopoulos - Nikolaos D. Macheras - Spyridon M. Tzaninis

On the equivalence of various definitions of mixed Poisson processes

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Year, pages: 2019, 453 - 468
Keywords: mixed Poisson process, mixed renewal process, disintegration, Markov property

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Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of ``canonical" probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

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ISO 690:
Lyberopoulos, D., Macheras, N., Tzaninis, S. 2019. On the equivalence of various definitions of mixed Poisson processes. In Mathematica Slovaca, vol. 69, no.2, pp. 453-468. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0238

APA:
Lyberopoulos, D., Macheras, N., Tzaninis, S. (2019). On the equivalence of various definitions of mixed Poisson processes. Mathematica Slovaca, 69(2), 453-468. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0238

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Published: 27. 3. 2019