Geodesic
Necessary condition for the regularity of branching processes
Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 389-396.

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A scheme of branching processes with conversions dependent on the age of the particles is discussed. Necessary conditions are found which must be satisfied by the distribution function of the particle lifetimes and the generating function for the number of descendants of a particle in processes that involve at any time with probability a finite number of particles. 
@article{MZM_1970_7_4_a2,
     author = {B. A. Sevast'yanov},
     title = {Necessary condition for the regularity of branching processes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {389--396},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a2/}
}
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B. A. Sevast'yanov. Necessary condition for the regularity of branching processes. Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 389-396. http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a2/