Geodesic
THE MODIFICATION OF THE GALTON-WATSON PROCESS
Acta mathematica Universitatis Comenianae, Tome 65 (1996) no. 1 
J. Kalas. THE MODIFICATION OF THE GALTON-WATSON PROCESS. Acta mathematica Universitatis Comenianae, Tome 65 (1996) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1996_65_1_a10/
@article{AMUC_1996_65_1_a10,
     author = {J. Kalas},
     title = {THE {MODIFICATION} {OF} {THE} {GALTON-WATSON} {PROCESS}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1996},
     volume = {65},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1996_65_1_a10/}
}
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Voir la notice de l'article provenant de la source Comenius University

In the paper we study the following modification of the classical Galton-Watson process. We suppose, starting with the first generation, that a particle of some generation ``lives to see'' the time of generating of the random number of new particles with the probability $p$. It is shown that the probability of the destruction of the population is equal to the smallest root of the equation $F(p\cdot s + q) = s$ ($q=1-p$).