Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 69, Issue 2

Issues

On the equivalence of various definitions of mixed poisson processes

Demetrios P. Lyberopoulos
  • Department of Statistics & Insurance Science University of Piraeus, 80 Karaoli and Dimitriou street 18534, Piraeus, Greece
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Nikolaos D. Macheras
  • Department of Statistics & Insurance Science University of Piraeus, 80 Karaoli and Dimitriou street 18534, Piraeus, Greece
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Spyridon M. Tzaninis
  • Department of Statistics & Insurance Science University of Piraeus, 80 Karaoli and Dimitriou street 18534, Piraeus, Greece
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2019-03-19 | DOI: https://doi.org/10.1515/ms-2017-0238

Abstract

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.

MSC 2010: Primary 60G55; Secondary 28A50; 28A35; 60G05; 60K05; 60J27; 91B30

Keywords: mixed Poisson process; mixed renewal process; disintegration; Markov property

References

About the article

Received: 2017-06-19

Accepted: 2018-06-05

Published Online: 2019-03-19

Published in Print: 2019-04-24


(Communicated by Gejza Wimmer)


Citation Information: Mathematica Slovaca, Volume 69, Issue 2, Pages 453–468, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0238.

Export Citation

© 2019 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in