Geodesic
On the ratio between the maximal and
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 435-452 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\{\xi_n\}$ be a critical branching process in a random environment. Under some restrictions on the characteristics of the process, we show that the ratio of $\sum_{i=0}^n\xi_i$ to $\max_{0\leqq i\leqq n}\xi_i$, given $\{\xi_n>0\}$, converges in distribution as $n\to\infty$ to a random variable taking on values in $(1,+\infty)$.
Keywords: branching process in a random environment, conditional random walk, conditional limit theorems. 
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V. I. Afanasyev. On the ratio between the maximal and. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 435-452. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a0/

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