Geodesic
Limit theorem for a supercritical Galton–Watson process
Matematičeskie zametki, Tome 18 (1975) no. 1, pp. 123-128 
I. S. Badalbaev. Limit theorem for a supercritical Galton–Watson process. Matematičeskie zametki, Tome 18 (1975) no. 1, pp. 123-128. http://geodesic.mathdoc.fr/item/MZM_1975_18_1_a15/
@article{MZM_1975_18_1_a15,
     author = {I. S. Badalbaev},
     title = {Limit theorem for a~supercritical {Galton{\textendash}Watson} process},
     journal = {Matemati\v{c}eskie zametki},
     pages = {123--128},
     year = {1975},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_1_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mu_n$, $n=0,1,\dots$ be a Galton–Watson process, and $\tau_x+1$ the instant of first crossing of the level $x$ by the process. A limit theorem is proved for the joint distribution of the random variables $$ \tau_x,\quad x-\mu_{\tau_x},\quad\mu_{\tau_x+1}-x\quad(x\to\infty) $$ on the assumption that $M\mu_1\ln(1+\mu_1)<\infty$.