О номерах поколений в ветвящемся процессе с произвольным множеством типов частиц
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 452-467
Voir la notice de l'article provenant de la source Math-Net.Ru
The asymptotic behaviour of the ratio $\xi_t(S)$ of the number of particles, whose types are in a given set $S$ and ages do not exceed $at+zb\sqrt t$, where $t$ denotes the time and $a$ and $b$ are some parameters, to the total number of particles with the types in $S$ is studied. It is shown that, for supercritical processes,
$$
\xi_t(S)\underset{t\to\infty}\longrightarrow\Phi(z),
$$
where $\Phi$ is the distribution function of $N(0,1)$.
@article{TVP_1969_14_3_a4,
author = {B. P. Harlamov},
title = {{\CYRO} {\cyrn}{\cyro}{\cyrm}{\cyre}{\cyrr}{\cyra}{\cyrh} {\cyrp}{\cyro}{\cyrk}{\cyro}{\cyrl}{\cyre}{\cyrn}{\cyri}{\cyrishrt} {\cyrv} {\cyrv}{\cyre}{\cyrt}{\cyrv}{\cyrya}{\cyrshch}{\cyre}{\cyrm}{\cyrs}{\cyrya} {\cyrp}{\cyrr}{\cyro}{\cyrc}{\cyre}{\cyrs}{\cyrs}{\cyre} {\cyrs} {\cyrp}{\cyrr}{\cyro}{\cyri}{\cyrz}{\cyrv}{\cyro}{\cyrl}{\cyrsftsn}{\cyrn}{\cyrery}{\cyrm} {\cyrm}{\cyrn}{\cyro}{\cyrzh}{\cyre}{\cyrs}{\cyrt}{\cyrv}{\cyro}{\cyrm} {\cyrt}{\cyri}{\cyrp}{\cyro}{\cyrv} {\cyrch}{\cyra}{\cyrs}{\cyrt}{\cyri}{\cyrc}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {452--467},
publisher = {mathdoc},
volume = {14},
number = {3},
year = {1969},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a4/}
}
TY - JOUR AU - B. P. Harlamov TI - О номерах поколений в ветвящемся процессе с произвольным множеством типов частиц JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1969 SP - 452 EP - 467 VL - 14 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a4/ LA - ru ID - TVP_1969_14_3_a4 ER -
B. P. Harlamov. О номерах поколений в ветвящемся процессе с произвольным множеством типов частиц. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 452-467. http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a4/