Geodesic
A~functional limit theorem for a critical branching process in a random environment
Diskretnaya Matematika, Tome 13 (2001) no. 4, pp. 73-91.

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Let $\{\xi_n\}$ be a critical branching process in a random environment, and let $m_n$ be the mathematical expectation of $\xi_n$ under the condition that the random environment is fixed. We prove a theorem on convergence of the sequence of branching processes $\{\xi_{[nt]}/m_{[nt]},\ t\in(0,1] \mid \xi_n>0\}$ as $n\to\infty$ in distribution in the corresponding functional space. This theorem extends the earlier result of the author proved under the assumption that the generating function of the number of offspring is linear-fractional. 
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V. I. Afanasyev. A~functional limit theorem for a critical branching process in a random environment. Diskretnaya Matematika, Tome 13 (2001) no. 4, pp. 73-91. http://geodesic.mathdoc.fr/item/DM_2001_13_4_a4/

[1] Afanasev V. I., “Novaya predelnaya teorema dlya kriticheskogo vetvyaschegosya protsessa v sluchainoi srede”, Diskretnaya matematika, 9:3 (1997), 52–67 | MR

[2] Afanasev V. I., “Predelnye teoremy dlya umerenno dokriticheskogo vetvyaschegosya protsessa v sluchainoi srede”, Diskretnaya matematika, 10:1 (1998), 141–157 | MR

[3] Afanasev V. I., “Predelnye teoremy dlya promezhutochno dokriticheskogo i strogo dokriticheskogo vetvyaschikhsya protsessov v sluchainoi srede”, Diskretnaya matematika, 13:1 (2001), 132–157

[4] Kozlov M. V., Teoriya veroyatnostei i ee primeneniya, 21, no. 4, 1976 | MR | Zbl

[5] Afanasev V. I., “Predelnaya teorema dlya kriticheskogo vetvyaschegosya protsessa v sluchainoi srede”, Diskretnaya matematika, 5:1 (1993), 45–58 | MR

[6] Borovkov K. A., Vatutin V. A., “Reduced critical branching processes in random environment”, Stoch. Proc. Appl., 71 (1997), 225–240 | DOI | MR | Zbl

[7] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, Moskva, 1977 | MR

[8] Geiger J., Kersting G., “The survival probability of a critical branching process in random environment”, Teoriya veroyatnostei i ee primeneniya, 45:3 (2000), 607–615 | MR | Zbl