Skip to main content
SpringerLink
Log in

Moments and order statistics of extinction times in multitype branching processes and their relation to random selection models

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We investigate the circumstances under which the moments of the order statistics of the extinction times of a set of independent branching processes exist. This extends a result of Schuster and Sigmund,Bull. math. Biol. 46, 11–17, 1984, which was found in a special random selection model. Furthermore we discussed existence of the expectation of extinction times of multitype branching processes and extend well known results for irreducible processes to the reducible case.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Athreya, K. B. and P. E. Ney. 1972.Branching Processes. Springer, Berlin.

    Google Scholar 

  • Cox, D. R. and D. V. Hinkley. 1974.Theoretical Statistics. Chapman-Hall, London.

    Google Scholar 

  • Gassner, B. 1984. Ein stochastisches Modell für die fehlerhafte molekulare Replikation von Nukleinsäuren, Ph.D. thesis, University of Vienna.

  • Harris, T. E. 1963.The Theory of Branching Processes. Springer, Berlin.

    Google Scholar 

  • Kimura, M. 1982.Molecular Evolution, Protein Polymorphism and the Neutral Theory. Springer, Berlin.

    Google Scholar 

  • Schuster, P. and K. Sigmund (1984a). “Random Selection—A Simple Model Based on Linear Birth and Death Processes.”Bull. math. Biol. 46, 11–17.

    MATH  Google Scholar 

  • Schuster, P. and K. Sigmund 1984b. “Random Selection and the Neutral Theory—Sources of Stochasticity in Replication.” InStochastic Phenomena and Chaotic, Behaviour in Complex Systems. Ed. P. Schuster. Springer Series in Synergetics, No. 21.

  • Sewastjanow, B. A. 1975.Verzweigungsprozesse. Oldenbourg, München.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Ökonometrie und Operations Research, University of Technology, Argentinierstr. 8, A-1040, Vienna, Austria

    B. M. Pötscher

Authors
  1. B. M. Pötscher
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pötscher, B.M. Moments and order statistics of extinction times in multitype branching processes and their relation to random selection models. Bltn Mathcal Biology 47, 263–272 (1985). https://doi.org/10.1007/BF02460035

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460035

Keywords

Search

Navigation