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On the equivalence of various definitions of mixed poisson processes

Lyberopoulos, Demetrios P. ; Macheras, Nikolaos D. ; Tzaninis, Spyridon M.

Mathematica Slovaca, 2019-04, Vol.69 (2), p.453-468 [Periódico revisado por pares]

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Título:
On the equivalence of various definitions of mixed poisson processes
Autor: Lyberopoulos, Demetrios P. ; Macheras, Nikolaos D. ; Tzaninis, Spyridon M.
Assuntos: 28A35 ; 60G05 ; 60J27 ; 60K05 ; 91B30 ; disintegration ; Equivalence ; Markov property ; mixed Poisson process ; mixed renewal process ; Poisson density functions ; Primary 60G55 ; Process parameters ; Random variables ; Secondary 28A50 ; Statistical analysis
É parte de: Mathematica Slovaca, 2019-04, Vol.69 (2), p.453-468
Descrição: 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.
Editor: Heidelberg: De Gruyter
Idioma: Inglês;Tcheco;Francês;Alemão;Russo

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