Geodesic
How many families survive for a long time?
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 709-732 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\{ Z_{k},k=0,1,\ldots\} $ be a critical branching process in a random environment generated by a sequence of independent and identically distributed random reproduction laws, and let $Z_{p,n}$ be the number of particles at time $p\le n$ having a positive offspring number at time $n$. A theorem is proved describing the limiting behavior, as $n\rightarrow \infty $, of the distribution of a properly scaled process $\log Z_{p,n}$ under the assumptions $Z_{n}>0$ and $p\ll n$.
Keywords: branching processes, random environment, reduced processes, conditional limit theorems.
Mots-clés : Lévy processes 
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V. A. Vatutin; E. E. D'yakonova. How many families survive for a long time?. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 709-732. http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a4/

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