Geodesic
Arcsine law for branching processes in a~random environment and Galton--Watson processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 449-464

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Two closely related results are established. A given critical branching process in a random environment attains a high level and spends at that level a part of its life obeying the arcsine law. If a critical Galton–Watson process survives up to a distant moment, then the ratio of the total number of individuals of the future generations to the total number of individuals ever born in the process obeys the arcsine law.
Keywords: branching process in a random environment, Galton–Watson process, stopped random walk, conditional invariance principle, conditional limit theorems
Mots-clés : arcsine law. 
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     author = {V. I. Afanasyev},
     title = {Arcsine law for branching processes in a~random environment and {Galton--Watson} processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {449--464},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a0/}
}
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V. I. Afanasyev. Arcsine law for branching processes in a~random environment and Galton--Watson processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 449-464. http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a0/