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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 4, Pages 845–853
(Mi tvp3429)
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This article is cited in 3 scientific papers (total in 3 papers)
Short Communications
Moment asymptotics for branching processes close to critical ones
О. V. V'yugin Moscow
Abstract:
We consider an age-dependent branching process with $n$ different types of particles. Let $\mu_j^i(t)$ be the number of particles of type $j$ at time $t$ if the process started from a single particle of type $i$. Let $A$ be the matrix of the process, and let $R$ be the Perron eigenvalue of $A$. We obtain an asymptotics of $A_j^i(t)=\mathbf M\mu_j^i(t)$ and $B_{jk}^i(t)=\mathbf M\mu_j^i(t)(\mu_k^i(t)-\delta_j^k)$ as $t\to\infty$, $R\to 1$ in a compact matrix class $\mathfrak A=\{A\}$.
Received: 21.04.1975
Citation:
О. V. V'yugin, “Moment asymptotics for branching processes close to critical ones”, Teor. Veroyatnost. i Primenen., 21:4 (1976), 845–853; Theory Probab. Appl., 21:4 (1977), 825–833
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https://www.mathnet.ru/eng/tvp3429 https://www.mathnet.ru/eng/tvp/v21/i4/p845
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Abstract page: | 140 | Full-text PDF : | 71 |
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