Geodesic
On the additive functionals of branching processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 2, pp. 389-394

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We define the additive functionals on the trajectories of branching processes. It is shown that in the critical and supercritical cases under the condition of non-extinction the value of the functional is asymptotically linearly dependent on the number of particles. Some examples are given. 
@article{TVP_1979_24_2_a12,
     author = {V. M. \v{S}urenkov},
     title = {On the additive functionals of branching processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {389--394},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_2_a12/}
}
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V. M. Šurenkov. On the additive functionals of branching processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 2, pp. 389-394. http://geodesic.mathdoc.fr/item/TVP_1979_24_2_a12/