Geodesic
A condition for the extinction of a bounded branching process
Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 9-18

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A subcritical Galton–Watson process is investigated under the condition that the number of particles is bounded above (“superfluous” particles are annihilated). A necessary and sufficient condition is obtained for the probability of extinction of such a process to be equal to unity. 
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     author = {A. M. Zubkov},
     title = {A condition for the extinction of a bounded branching process},
     journal = {Matemati\v{c}eskie zametki},
     pages = {9--18},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a1/}
}
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A. M. Zubkov. A condition for the extinction of a bounded branching process. Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 9-18. http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a1/