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Bisexual Galton-Watson Branching Processes in Random Environments

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Abstract

In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment process. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established.

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References

  1. Agresti, A. On the extinction times of varying and random environment branching processes. J. Appl. Prob., 12: 39–46 (1975)

    Article  MathSciNet  Google Scholar 

  2. Alsmeyer, G., Rosler, U. The bisexual Galton-Waston process with promiscuous mating: Extinction probabilities in the supercritical case. Ann. Appl. Prob., 6: 922–939 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bruss, F.T. A note on extinction criteria for bisexual Galton-Watson processes. J. Appl. Prob., 21: 915–919 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  4. Church, J.D. On the infinite composition products generating functions. Z. Wahrscheinlichkeitsth 19: 243–256 (1971)

    Article  MathSciNet  Google Scholar 

  5. Daley, D.J. Extinction conditions for certain bisexual Galton-Watson processes. Z. Wahr., 9: 315–322 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  6. Daley, D.J., Hull, D.A., Taylor, J.M. Bisexual Galton-Watson branching processes with superadditive mating funtions. J. Appl. Prob., 23: 585–600 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  7. González, M., Molina, M. On the limit behaviour of a supercritical bisexual Galton-Watson branching processes. J. Appl. Prob., 33: 960–967 (1996)

    Article  MATH  Google Scholar 

  8. González, M., Molina, M. On the L 2-convergence of a superadditive Bisexual Galton-Watson branching processes. J. Appl. Prob., 34: 575–582 (1997)

    Article  MATH  Google Scholar 

  9. González, M., Molina, M., Mota, M. Limit behaviour for a subcritical bisexual Galton-Watson branching process with immigration. Stat. Probab. Letts., 49: 19–24 (2000)

    Article  MATH  Google Scholar 

  10. González, M., Molina, M., Mota, M. Bisexual Galton-Watson branching process with immigration of females and males: Asymptotic behaviour. Markov Process. Relat. Fields, 8: 651–663 (2002)

    MATH  Google Scholar 

  11. González, M. Molina, M., Mota, M. On the limit behaviour of a supercritical bisexual Galton-Watson branching process with immigration of mating units. Stoch. Anal., 19: 933–945 (2001)

    MATH  Google Scholar 

  12. Hille, E., Phillips, R. Functional analysis and semi-groups. Am. Math. Soc. Colloquium Publications, Vol. XXXI, 1957

  13. Hull, D.M. A necessary condition for extinction in those bisexual Galton-Watson branching processes governed by superadditive mating funtions. J. Appl. Prob., 19: 847–850 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  14. Molina, M., Mota, M., Ramos, A. Bisexual Galton-Watson branching process with population-size-dependent mating. J. Appl. Prob., 39: 479–490 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Molina, M., Mota, M., Ramos, A. Bisexual Galton-Waston branching process in varying environments. Stoch. Anal. Appl., 21: 1353–1367 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Smith, W.L., Wilkinson, W.E. On branching processes in random environments. Ann. Math. Statist., 40: 814–827 (1969)

    MathSciNet  Google Scholar 

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  1. School of Mathematical Sciences, Nankai University, Tianjin, 300071, China

    Shi-xia Ma

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  1. Shi-xia Ma
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Ma, Sx. Bisexual Galton-Watson Branching Processes in Random Environments. Acta Math. Appl. Sin, Engl. Ser. 22, 419–428 (2006). https://doi.org/10.1007/s10255-006-0317-4

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  • DOI: https://doi.org/10.1007/s10255-006-0317-4

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