Self-decomposable discrete distributions and branching processes

  • K. van Harn
  • F. W. Steutel
  • W. Vervaat
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)


Self-decomposable distributions are known to be absolutely continuous. In this note analogues of the concept of self-decomposability are proposed for distributions on the set ℕ0 of nonnegative integers. To each of them corresponds an analogue of multiplication (in distribution) that preserves ℕ0-valuedness and is characterized by a composition semigroup of probability generating functions, such as occur in branching processes.


Nonnegative Integer Absolute Continuity Continuous Semigroup Probability Generate Function Divisible Distribution 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • K. van Harn
    • 1
  • F. W. Steutel
    • 2
  • W. Vervaat
    • 3
  1. 1.Wiskundig SeminariumVrije UniversiteitAmsterdam
  2. 2.Onderafd. der Wiskunde Techn. HogeschoolEindhoven
  3. 3.Math. InstituutKath. UniversiteitNijmegen

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