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Self-decomposable discrete distributions and branching processes

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Part of the Lecture Notes in Mathematics book series (LNM,volume 861)

Abstract

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.

Keywords

  • Nonnegative Integer
  • Absolute Continuity
  • Continuous Semigroup
  • Probability Generate Function
  • Divisible Distribution

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References

  1. Athreya, K.B. & Ney, P.E., Branching processes. Springer, Berlin 1972.

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© 1981 Springer-Verlag

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van Harn, K., Steutel, F.W., Vervaat, W. (1981). Self-decomposable discrete distributions and branching processes. In: Dugué, D., Lukacs, E., Rohatgi, V.K. (eds) Analytical Methods in Probability Theory. Lecture Notes in Mathematics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097314

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  • DOI: https://doi.org/10.1007/BFb0097314

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10823-8

  • Online ISBN: 978-3-540-36785-7

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