Geodesic
Limit theorems for the total number of descendants for the Galton–Watson branching process
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 503-528 Cet article a éte moissonné depuis la source Math-Net.Ru

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The main results of the present paper deal with the asymptotic behavior of the conditional distribution for the whole number of descendants $S_n $ of a single particle in the Galton–Watson process with respect to the condition that the process degenerates at time n and the expectation for the number of particles generated by one particle tends to 1 as $n \to \infty $.
Keywords: the Galton–Watson branching processes, processes close to critical ones, degeneracy, asymptotic behavior of the total number of descendants. 
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     author = {A. V. Karpenko and S. V. Nagaev},
     title = {Limit theorems for the total number of descendants for the {Galton{\textendash}Watson} branching process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {503--528},
     year = {1993},
     volume = {38},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a2/}
}
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A. V. Karpenko; S. V. Nagaev. Limit theorems for the total number of descendants for the Galton–Watson branching process. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 3, pp. 503-528. http://geodesic.mathdoc.fr/item/TVP_1993_38_3_a2/