Publication: On largest offspring in a critical branching process with finite variance
On largest offspring in a critical branching process with finite variance
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Bertoin, J. (2013). On largest offspring in a critical branching process with finite variance. Journal of Applied Probability, 50(3), 791–800. https://doi.org/10.1239/jap/1378401236
Abstract
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Abstract
Continuing the work in Bertoin (2011) we study the distribution of the maximal number Xk of offspring amongst all individuals in a critical Galton-Watson process started with k ancestors, treating the case when the reproduction law has a regularly varying tail F with index -α for α < 2 (and, hence, finite variance). We show that Xk suitably normalized converges in distribution to a Fréchet law with shape parameter α/2; this contrasts sharply with the case 1 < α < 2 when the variance is infinite. More generally, we obtain a weak limi
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- Bertoin, Jean
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Citations
Bertoin, J. (2013). On largest offspring in a critical branching process with finite variance. Journal of Applied Probability, 50(3), 791–800. https://doi.org/10.1239/jap/1378401236
