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Conditions for the unlimited growth in multitype population size dependent galton-watson processes

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Abstract

Sufficient conditions are given for the unlimited growth or otherwise in multitype population size dependent Galton-Watson processes. These conditions are given in terms of moments of offspring distributions and extend known conditions for processes with one type.

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Literature

  • Becker, N. 1976. Estimation for an epidemic model.Biometrics,32, 769–777.

    Article  MATH  Google Scholar 

  • Berman, A. and R. J. Plemmons. 1979.Nonnegative Matrices in the Mathematical Sciences. New York: Academic Press.

    Google Scholar 

  • Fujimagari, T. 1971. Controlled Galton-Watson process and its asymptotic behavior.Kodai Math. Sem. Rep.,27, 11–18.

    MathSciNet  Google Scholar 

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

    Google Scholar 

  • Harris, J. W. and R. W. Kellermeyer. 1971.The Red Cell: Production, Metabolism, Destruction, Normal and Abnormal. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Hopfner, R. 1985. On some classes of population-size-dependent Galton-Watson processes.J. appl. Prob.,22, 25–36.

    Article  MathSciNet  Google Scholar 

  • Kesten, H. 1976. Recurrence criteria for multidimensional Markov chains and multidimensional linear birth and death processes.Adv. appl. Prob.,8, 58–87.

    Article  MATH  MathSciNet  Google Scholar 

  • Kesting, G. 1986. On recurrence and transience of growth models.J. appl. Prob.,23, 614–625.

    Article  Google Scholar 

  • Klebaner, F. C. 1984. On population-size-dependent branching processes.Adv. appl. Prob. 16, 30–55.

    Article  MATH  MathSciNet  Google Scholar 

  • Klebaner, F. C. 1989. Linear growth in near critical population size dependent multitype Galton-Watson processes.J. appl. Prob., in press.

  • Levy, J. B. 1979. Transience and recurrence of state-dependent branching processes with an immigration component.Adv. appl. Prob. 11, 73–92.

    Article  MATH  Google Scholar 

  • Maelzer, D. A. 1970. The regression of logN(n+1) on logN(n) as a test of density dependence.Ecology 51, 810–822.

    Article  Google Scholar 

  • Mode, C. 1971.Multitype Branchina Processes. Amsterdam: Elsevier.

    Google Scholar 

  • Rittgen, W. and P. Tautu. 1976. Branching models for cell cycle. InMathematical Models in Medicine (Lecture notes on Biomathematics, Vol. 11), pp. 109–126. Berlin: Springer.

    Google Scholar 

  • Rittgen, W. 1983. Controlled branching processes and their application to normal and malignant haematopoieses.Bull. math. Biol.,45, 617–626.

    Article  MATH  Google Scholar 

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Authors and Affiliations

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

    Fima C. Klebaner

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  1. Fima C. Klebaner
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Klebaner, F.C. Conditions for the unlimited growth in multitype population size dependent galton-watson processes. Bltn Mathcal Biology 52, 527–534 (1990). https://doi.org/10.1007/BF02462265

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  • DOI: https://doi.org/10.1007/BF02462265

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