Blätter der DGVFM

, Volume 18, Issue 2, pp 107–110 | Cite as

Martingale characteristics of mixed poisson processes

  • Dietmar Pfeifer


We investigate which kind of transformations of the occurrence times of mixed Poisson processes give rise to martingales, and how such transformations can be used to characterize mixed Poisson processes among the class of pure birth processes by martingale properties.


Monotonic Function Occurrence Time Birth Process Accident Statistics Martingale Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


In der vorliegenden Arbeit wird untersucht, welche Transformationen der Eintrittszeitpunkte gemischter Poisson-Prozesse zu Martingalen führen, und wie solche Transformationen zur Charakterisierung gemischter Poisson-Prozesse in der Klasse der Geburtsprozesse durch Martingaleigenschaften herangezogen werden können.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Albrecht, P. (1985): Mixed Poisson processes. In: Encylopedia of Statistical Sciences, Vol. 6. Wiley, N.Y.Google Scholar
  2. Bernstein, S. (1928): Su les fonctions absolument monotones. Acta Math. 51, 1–66CrossRefGoogle Scholar
  3. Heller, U., andPfeifer, D. (1987): A martingale characterization of mixed Poisson processes. J. Appl. Prob. 24, 246–251MATHCrossRefMathSciNetGoogle Scholar
  4. Lundberg, O. (1940): On Random Processes and Their Application to Sickness and Accident Statistics. Reprinted (1964) by Almqvist and Wiksell, UppsalaGoogle Scholar
  5. Pfeifer, D. (1982): The structure of elementary pure birth processes. J. Appl. Prob. 19, 664–667MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© DAV/DGVFM 1987

Authors and Affiliations

  • Dietmar Pfeifer
    • 1
  1. 1.Aachen

Personalised recommendations