Skip to main content
SpringerLink
Log in
Book cover

Classical and Modern Branching Processes pp 165–169Cite as

Population and Density Dependent Branching Processes

  • Chapter

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 84))

Abstract

This paper gives results on branching processes in which the offspring distribution is a function of the current population size or density. Some interesting phenomena in such processes which do not occur in the classical models are given.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Friedlin M.I. and Wentzel A.D. (1984) Random Pertrwbations of Dynamical Systems. Springer.

    Book  Google Scholar 

  2. Hopfner R. (1985) On some classes of population size dependent Galton-Watson processes. J. Appl. Probab. 22, 25–36.

    Article  MathSciNet  Google Scholar 

  3. Kersting G. (1992) Asymptotic F distribution for stochastic difference equation. Stock. Proc. Appl. 40, 15–28.

    Article  MathSciNet  MATH  Google Scholar 

  4. Kifer Y. (1990) A discrete time version of the Wentzell-Freidlin theory. Ann. Probab. 18, 1676–1692.

    Article  MathSciNet  MATH  Google Scholar 

  5. Klebaner F.C. (1983) Population size dependent branching process with linear rate of growth. J. Appl. Probab. 20, 242–250.

    Article  MathSciNet  MATH  Google Scholar 

  6. Klebaner F.C. (1984) On population size dependent branching processes. Adv. Appl. Probab. 16, 30–55.

    Article  MathSciNet  MATH  Google Scholar 

  7. Klebaner F.C. (1984) Geometric growth in population-size-dependent branching processes. J. Appl. Probab. 21, 40–49.

    Article  MathSciNet  MATH  Google Scholar 

  8. Klebaner F.C. (1985) A limit theorem for population-size-dependent branching processes. J. Appl. Probab. 22, 48–57.

    Article  MathSciNet  MATH  Google Scholar 

  9. Klebaner F.C. (1989) Stochastic difference equations and generalized gamma distribution. Ann. Probab. 17, 178–188.

    Article  MathSciNet  MATH  Google Scholar 

  10. Klebaner F.C. (1993) Population dependent branching processes with a threshold. Stoch. Proc. Appl. 46, 115–127.

    Article  MathSciNet  MATH  Google Scholar 

  11. Klebaner F.C. and Nerman O. (1994) Autoregressive approximation in branching processes with a threshold. Stoch. Proc. Appl. 51, 1–7.

    Article  MathSciNet  MATH  Google Scholar 

  12. Klebaner F.C. and Zeitouni O. (1994) The exit problem for a class of period doubling systems. Ann. Appl. Probab. 4, 1188–1205.

    Article  MathSciNet  MATH  Google Scholar 

  13. Kuster P. (1985) Asymptotic growth of controlled Galton-Watson processes. Ann. Probab. 13, 1157–1178.

    Article  MathSciNet  Google Scholar 

  14. Thompson M.T. and Stewart H.B. (1986) Nonlinear Dynamics and Chaos. Wiley.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statistics Department, University of Melbourne, Parkville, Victoria, 3052, Australia

    F. C. Klebaner

Authors
  1. F. C. Klebaner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Iowa State University, Ames, IA, 50011, USA

    Krishna B. Athreya

  2. School of Mathematics and Computing Science, Chalmers University of Technology, Gothenburg University, Gothenburg, S-412 96, Sweden

    Peter Jagers

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Klebaner, F.C. (1997). Population and Density Dependent Branching Processes. In: Athreya, K.B., Jagers, P. (eds) Classical and Modern Branching Processes. The IMA Volumes in Mathematics and its Applications, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1862-3_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1862-3_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7315-8

  • Online ISBN: 978-1-4612-1862-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation