Geodesic
A new limit theorem for a critical branching process in a random environment
Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 52-67

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Let $\{\xi_n\}$ be a critical branching process in random environment with linear-fractional generating functions, $m_n$ be the conditional expectation of $\xi_n$ with respect to random environment. We prove a theorem on convergence of the sequence of random processes $\{\xi_{[nt]}/m_{[nt]},\ t\in(0,1] \mid \xi_n>0\}$ as $n\to\infty$ in distribution in the corresponding functional space. 
@article{DM_1997_9_3_a4,
     author = {V. I. Afanasyev},
     title = {A new limit theorem for a critical branching process in a random environment},
     journal = {Diskretnaya Matematika},
     pages = {52--67},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_3_a4/}
}
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V. I. Afanasyev. A new limit theorem for a critical branching process in a random environment. Diskretnaya Matematika, Tome 9 (1997) no. 3, pp. 52-67. http://geodesic.mathdoc.fr/item/DM_1997_9_3_a4/