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Teoriya Veroyatnostei i ee Primeneniya, 1971, Volume 16, Issue 2, Pages 201–216
(Mi tvp2125)
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This article is cited in 9 scientific papers (total in 9 papers)
Multidimensional renewal equations and moments of branching processes
B. A. Sevast'yanova, V. P. Čistyakov a Moscow
Abstract:
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.
Received: 06.07.1970
Citation:
B. A. Sevast'yanov, V. P. Čistyakov, “Multidimensional renewal equations and moments of branching processes”, Teor. Veroyatnost. i Primenen., 16:2 (1971), 201–216; Theory Probab. Appl., 16:2 (1971), 199–214
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