Geodesic
Conditions of extinction of a $\varphi$-branching process with random~$\varphi$
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 433-440

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We introduce a new class of $\varphi$-branching processes, in which the controlling functions $\varphi_t(n)$ $(t,n=0,1,2,\dots)$ are random variables. We give conditions on $\varphi_t(n)$ sufficient for extinction or non-extinction of the $\varphi$-process. 
@article{TVP_1975_20_2_a22,
     author = {N. M. Yanev},
     title = {Conditions of extinction of a $\varphi$-branching process with random~$\varphi$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {433--440},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a22/}
}
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N. M. Yanev. Conditions of extinction of a $\varphi$-branching process with random~$\varphi$. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 433-440. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a22/