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Stochastic Analysis and Applications Volume 19, 2001 - Issue 6
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Original Articles

On the limit behavior of a supercritical bisexual Galton–Watson branching process with immigration of mating units

M. González Department of Mathematics, Faculty of Sciences, University of Extremadura, Badajoz, 06071, Spain
,
M. Molina Department of Mathematics, Faculty of Sciences, University of Extremadura, Badajoz, 06071, Spain
&
M. Mota Department of Mathematics, Faculty of Sciences, University of Extremadura, Badajoz, 06071, Spain
Pages 933-943 | Published online: 15 Feb 2007

REFERENCES

  • Asmussen , S. and Hering , H. 1983 . Branching Process Basel : Birkhaüser .
  • Bagley , J.H. 1986 . On the Asymptotic Properties of a Supercritical Bisexual Branching Process . J. Appl. Prob. , 23 : 820 – 826 .
  • Bruss , F.T. 1984 . A Note on Extinction Criteria for Bisexual Galton–Watson Branching Processes . J. Appl. Prob. , 21 : 915 – 919 .
  • Daley , D.J. 1968 . Extinction Condition for Bisexual Galton–Watson Branching Processes . Z. Wahrscheinlichkeitsth , 9 : 315 – 322 .
  • Daley , D.J. , Hull , D.M. and Taylor , J.M. 1986 . Bisexual Galton–Watson Branching Processes with Superadditive Mating Functions . J. Appl. Prob. , 23 : 585 – 600 .
  • González , M. and Molina , M. 1996 . On the Limit Behaviour of a Superadditive Bisexual Galton–Watson Branching Process . J. Appl. Prob. , 33 : 960 – 967 .
  • González , M. and Molina , M. 1997 . On the L 2-Convergence of a Superadditive Bisexual Galton–Watson Branching Process . J. Appl. Prob. , 34 : 575 – 582 .
  • González , M. and Molina , M. 1998 . On the Partial and Total Progeny of a Bisexual Galton–Watson Branching Process . Appl. Stoch. Models Data Anal. , 13 : 225 – 232 .
  • González Fragoso , A. 1995 . Ratio Estimation for the Offspring Means of a Bisexual Galton–Watson Branching Process . Estadística , 47 ( 148–149 ) : 17 – 36 .
  • Hull , D.M. 1982 . A Necessary Condition for Extinction in those Bisexual Galton–Watson Branching Processes Governed by Superadditive Mating Functions . J. Appl. Prob. , 19 : 847 – 850 .
  • Hull , D.M. 1984 . Conditions for Extinction in Certain Bisexual Galton–Watson Branching Processes . J. Appl. Prob. , 21 : 414 – 418 .
  • Klebaner , F.C. 1985 . A Limit Theorem for Population-Size-Dependent Branching Processes . J. Appl. Prob. , 22 : 48 – 57 .
  • Molina , M. , González , M. and Mota , M. 1998 . Bayesian Inference for Bisexual Galton–Watson Processes . Commun. Statist.: Theory Methods , 27 : 1055 – 1070 .
  • Williams , D. 1991 . Probability with Martingales Cambridge : Cambridge University Press .

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