Skip to main content
SpringerLink
Log in

Self-decomposable discrete distributions and branching processes

  • Conference paper
  • First Online:
Analytical Methods in Probability Theory

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

  • 534 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Book  MATH  Google Scholar 

  2. Fisz, M. & Varadarajan, V.S., A condition for absolute continuity of infinitely divisible distribution functions. Z. Wahrscheinlichkeitstheorie verw. Gebiete 1 (1963), 335–339.

    Article  MathSciNet  MATH  Google Scholar 

  3. Forst, G., A characterization of self-decomposable probabilities on the half-line. Z. Wahrscheinlichkeitstheorie verw. Gebiete 49 (1979), 349–352.

    Article  MathSciNet  MATH  Google Scholar 

  4. van Harn, K., Classifying infinitely divisible distributions by functional equations. Math. Centre Tracts 103, Math. Centre, Amsterdam 1978.

    MATH  Google Scholar 

  5. Harris, T.E., The theory of branching processes. Springer, Berlin 1963.

    Book  MATH  Google Scholar 

  6. Steutel, F.W. & van Harn, K., Discrete analogues of self-decomposability and stability. Ann. Probability 7 (1979), 893–899.

    Article  MathSciNet  MATH  Google Scholar 

  7. Steutel, F.W., Vervaat, W. & Wolfe, S.J., Integer-valued branching processes with immigration. Forthcoming.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wiskundig Seminarium, Vrije Universiteit, Amsterdam

    K. van Harn

  2. Onderafd. der Wiskunde Techn. Hogeschool, Eindhoven

    F. W. Steutel

  3. Math. Instituut, Kath. Universiteit, Nijmegen

    W. Vervaat

Authors
  1. K. van Harn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. W. Steutel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. Vervaat
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Daniel Dugué Eugene Lukacs Vijay K. Rohatgi

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10823-8

  • Online ISBN: 978-3-540-36785-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation