2004
DOI: 10.1016/j.spa.2004.02.003
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Limit behaviour for a supercritical bisexual Galton–Watson branching process with population-size-dependent mating

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Cited by 16 publications
(17 citation statements)
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“…This asymptotic rate plays a major role in the research of the extinction probability, partial and total progeny and limiting evolution of a BPSDM, see Molina et al (2002Molina et al ( , 2004aMolina et al ( , 2004b.…”
Section: Remark 21mentioning
confidence: 99%
See 1 more Smart Citation
“…This asymptotic rate plays a major role in the research of the extinction probability, partial and total progeny and limiting evolution of a BPSDM, see Molina et al (2002Molina et al ( , 2004aMolina et al ( , 2004b.…”
Section: Remark 21mentioning
confidence: 99%
“…In particular, Molina et al (2002) introduced the class of bisexual processes with population-size dependent mating where, unlike other bisexual models, the function governing the mating is allowed to change in each generation depending on the total number of couples in the previous one. Some theory about such processes has been developed in Molina et al (2002Molina et al ( , 2004aMolina et al ( , 2004b.…”
Section: Introductionmentioning
confidence: 99%
“…The asymptotic behaviour of a BPSDM given P1 and P2 is studied in Molina et al . (2004), in which sufficient conditions for P3 are also provided.…”
Section: The Probabilistic Modelmentioning
confidence: 99%
“…With respect to (v), it is clear that . Then, since { r − n Z n } n ≥0 and { r − n ( F n , M n )} n ≥1 converge almost surely to W and r −1 W μ, respectively (see Molina et al ., 2004), considering P4, converges almost surely to μ on Q .…”
Section: Estimation Of the Offspring Mean Vectormentioning
confidence: 99%
“…Such a model has received some attention in the literature; see, for example, Rösler (1996, 2002), Bagley (1986), Bruss (1984), Daley et al (1986), González and Molina (1996, 1997), or Hull (1982. More recently, with the objective to model the probabilistic evolution of more complex two-sex populations, various classes of bisexual branching processes have been introduced and some theory about them developed; see, for instance, González et al (2000González et al ( , 2001, Molina et al (2002Molina et al ( , 2003Molina et al ( , 2004aMolina et al ( , 2004b or Xing and Wang (2005). We refer the reader to Hull (2003) for a survey about the literature associated with the bisexual branching processes.…”
Section: Introductionmentioning
confidence: 99%