Multidimensional renewal equations and moments of branching processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 201-216
Voir la notice de l'article provenant de la source Math-Net.Ru
We mean by a multidimensional renewal equation a system of equations
\begin{gather*}
X^l_m(x)=K^l_m(x)+\sum_{\alpha=1}^n\int_0^xX^\alpha_m(x-u)\,dF^l_\alpha(u)
\\
l=1,\dots,n;\quad m=1,\dots,N,
\end{gather*}
where $F^l_m(x)$ are non-decreasing right-continious non-negative functions, $F^l_m(0)=0$, ($l,m=1,\dots,n$) and $K^l_m(x)$, $l,=1,\dots,n$, $m=1,\dots,N$ are measurable bounded functions satisfying some conditions. The asymptotic behaviour of solution $X^l_m(x)$ is described in theorems 2.1–2.7. We use these theorems to investigate asymptotic behaviour of the first and second moments of age-dependent branching processes with $n$ types of particles.
@article{TVP_1971_16_2_a0,
author = {B. A. Sevast'yanov and V. P. \v{C}istyakov},
title = {Multidimensional renewal equations and moments of branching processes},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {201--216},
publisher = {mathdoc},
volume = {16},
number = {2},
year = {1971},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a0/}
}
TY - JOUR AU - B. A. Sevast'yanov AU - V. P. Čistyakov TI - Multidimensional renewal equations and moments of branching processes JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1971 SP - 201 EP - 216 VL - 16 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a0/ LA - ru ID - TVP_1971_16_2_a0 ER -
B. A. Sevast'yanov; V. P. Čistyakov. Multidimensional renewal equations and moments of branching processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 201-216. http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a0/