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A note on the probability of extinction in a class of population-size-dependent Galton-Watson processes

  • R. Höpfner (a1)

Abstract

In a class of population-size-dependent Galton-Watson processes where extinction does not occur with probability 1 we describe the rate of decay of qi (the probability that the process starting from i ancestors will become extinct) as the number i of ancestors increases.

The results are related to the asymptotic behavior of the Green's function of the critical Galton-Watson process with immigration.

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Corresponding author

Postal address: Institut für Mathematische Stochastik, Albert-Ludwigs-Universität, Hebelstr. 27, D-7800 Freiburg, West Germany.

References

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[1] Fujimagari, T. (1976) Controlled Galton-Watson process and its asymptotic behavior. Kodai Math. Sem. Rep. 27, 1118.
[2] Galambos, J. and Seneta, E. (1973) Regularly varying sequences. Proc. Amer. Math. Soc. 41, 110116.
[3] Höpfner, R. (1983) über einige Klassen von zustandsabhängigen Galton-Watson Prozessen. Dissertation, Fachbereich Mathematik, Johannes-Gutenberg-Universität Mainz.
[4] Höpfner, R. (1985) On some classes of population-size-dependent branching processes. J. Appl. Prob. 22, 2536.
[5] Ivanoff, B. G. and Seneta, E. (1985) The critical branching processes with immigration stopped at zero. J. Appl. Prob. 22, 223227.
[6] Klebaner, F. C. (1983) Population-size-dependent branching process with linear rate of growth. J. Appl. Prob. 20, 242250.
[7] Klebaner, F. C. (1984) On population-size-dependent branching processes. Adv. Appl. Prob. 16, 3055.
[8] Klebaner, F. C. (1984) Geometric rate of growth in population-size-dependent Galton-Watson processes. J. Appl. Prob. 21, 4049.
[9] Klebaner, F. C. (1985) A limit theorem for population-size-dependent branching processes. J. Appl. Prob. 22, 4857.
[10] Küster, P. (1985) Asymptotic growth of controlled Galton-Watson processes. Ann. Prob.
[11] Levy, J. B. (1979) Transience and recurrence of state-dependent branching processes with an immigration component. Adv. Appl. Prob. 11, 7392.
[12] Pakes, A. G. (1971) On the critical Galton-Watson process with immigration. J. Austral. Math. Soc. 12, 476482.
[13] Pakes, A. G. (1972) Further results on the critical Galton-Watson process with immigration. J. Austral. Math. Soc. 13, 277290.
[14] Roi, L. D. (1975) State-Dependent Branching Processes. Thesis, Purdue University.
[15] Seneta, H. and Tavaré, S. (1983) A note on models using the branching process with immigration stopped at zero. J. Appl. Prob. 20, 1118.
[16] Zubkov, A. M. (1972) Life periods of a branching process with immigration. Theory Prob. Appl. 17, 174183.

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A note on the probability of extinction in a class of population-size-dependent Galton-Watson processes

  • R. Höpfner (a1)

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