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On the L 2-convergence of a superadditive bisexual Galton-Watson branching process

  • M. González (a1) and M. Molina (a1)

Abstract

In this paper the L 2-convergence of a superadditive bisexual Galton–Watson branching process is studied. Necessary and sufficient conditions for the convergence of the suitably normed process are given. In the final section, a result about one of the most important bisexual models is proved.

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Postal address: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, 06071-Badajoz, Spain.

References

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Bagley, J. H. (1986) On the asymptotic properties of a supercritical bisexual branching process. J. Appl. Prob. 23, 820826.
Daley, D. J. (1968) Extinction condition for certain bisexual Galton-Watson branching processes. Z. Wahrscheinlichkeitsth. 9, 315322.
Daley, D. J., Hull, D. M. and Taylor, J. M. (1986) Bisexual Galton-Watson branching processes with superadditive mating functions. J. Appl. Prob. 23, 585600.
González, M. and Molina, M. (1996) On the limit behaviour of a superadditive bisexual Galton-Watson branching process. J. Appl. Prob 33, 960967.
Hille, E. and Phillips, R. S. (1957) Functional Analysis and Semi-Groups (Amer. Math. Soc. Colloq. XXXI). AMS, Providence, RI.
Klebaner, F. C. (1984) Geometric rate of growth in population-size-dependent branching processes. J. Appl. Prob. 21, 4049.

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On the L 2-convergence of a superadditive bisexual Galton-Watson branching process

  • M. González (a1) and M. Molina (a1)

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