Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 387-394
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B. A. Sevast'yanov. Mathematical expectations of functions of sums of a random number of independent terms. Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 387-394. http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a2/
@article{MZM_1968_3_4_a2,
author = {B. A. Sevast'yanov},
title = {Mathematical expectations of functions of sums of a~random number of independent terms},
journal = {Matemati\v{c}eskie zametki},
pages = {387--394},
year = {1968},
volume = {3},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a2/}
}
TY - JOUR
AU - B. A. Sevast'yanov
TI - Mathematical expectations of functions of sums of a random number of independent terms
JO - Matematičeskie zametki
PY - 1968
SP - 387
EP - 394
VL - 3
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a2/
LA - ru
ID - MZM_1968_3_4_a2
ER -
%0 Journal Article
%A B. A. Sevast'yanov
%T Mathematical expectations of functions of sums of a random number of independent terms
%J Matematičeskie zametki
%D 1968
%P 387-394
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a2/
%G ru
%F MZM_1968_3_4_a2
Conditions are found which must be imposed on a function $g(x)$, in order that $Mg(\xi_1+\xi_2+\dots+\xi_\nu)<\infty$, if $Mg(\xi_i)<\infty$ and $Mg(\nu)<\infty$, $\nu,\xi_1,\xi_2,\dots,\xi_n,\dots$ being non-negative and independent, $\nu$ being integral, and $\{\xi_i\}$ being identically distributed. The result is applied to the theory of branching processes.
