Geodesic
Multidimensional renewal equations and moments of branching processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 2, pp. 201-216 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {1971},
     volume = {16},
     number = {2},
     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
UR  - http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a0/
LA  - ru
ID  - TVP_1971_16_2_a0
ER  - 
%0 Journal Article
%A B. A. Sevast'yanov
%A V. P. Čistyakov
%T Multidimensional renewal equations and moments of branching processes
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1971
%P 201-216
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1971_16_2_a0/
%G ru
%F TVP_1971_16_2_a0
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/