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Teor. Veroyatnost. i Primenen., 1971, Volume 16, Issue 2, Pages 201–216 (Mi tvp2125)  

This article is cited in 5 scientific papers (total in 5 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,…,n;\quad m=1,…,N, \end{gather*}
where $F^l_m(x)$ are non-decreasing right-continious non-negative functions, $F^l_m(0)=0$, ($l,m=1,…,n$) and $K^l_m(x)$, $l,=1,…,n$, $m=1,…,N$ 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.

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English version:
Theory of Probability and its Applications, 1971, 16:2, 199–214

Bibliographic databases:

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

Citation in format AMSBIB
\Bibitem{SevChi71}
\by B.~A.~Sevast'yanov, V.~P.~{\v C}istyakov
\paper Multidimensional renewal equations and moments of branching processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1971
\vol 16
\issue 2
\pages 201--216
\mathnet{http://mi.mathnet.ru/tvp2125}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=283893}
\zmath{https://zbmath.org/?q=an:0239.60079}
\transl
\jour Theory Probab. Appl.
\yr 1971
\vol 16
\issue 2
\pages 199--214
\crossref{https://doi.org/10.1137/1116021}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. B. Engibaryan, “Renewal theorems for a system of integral equations”, Sb. Math., 189:12 (1998), 1795–1808  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. M. S. Sgibnev, “Semimultiplicative estimates for the solution of the multidimensional renewal equation”, Izv. Math., 66:3 (2002), 595–610  mathnet  crossref  crossref  mathscinet  zmath
    3. N. B. Engibaryan, “Conservative systems of integral convolution equations on the half-line and the entire line”, Sb. Math., 193:6 (2002), 847–867  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. N. B. Engibaryan, “Asymptotic and structural theorems for the Markov renewal equation”, Theory Probab. Appl., 48:1 (2004), 80–92  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. M. S. Sgibnev, “Exact asymptotic expansions for solutions of multi-dimensional renewal equations”, Izv. Math., 70:2 (2006), 363–383  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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