On maximum family size in branching processes

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On maximum family size in branching processes

Rahimov, Ibrahim; Yanev, George P.

Journal of applied probability, 09/1999, Volume: 36, Issue: 3

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The number Y n of offspring of the most prolific individual in the nth generation of a Bienaymé–Galton–Watson process is studied. The asymptotic behaviour of Y n as n → ∞ may be viewed as an extreme value problem for i.i.d. random variables with random sample size. Limit theorems for both Y n and EY n provided that the offspring mean is finite are obtained using some convergence results for branching processes as well as a transfer limit lemma for maxima. Subcritical, critical and supercritical branching processes are considered separately.

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