V. P. Čistyakov, “Asymptotic behaviour of the non-extinction probability for a critical Branching process”, Teor. Veroyatnost. i Primenen., 16:4 (1971), 638–648; Theory Probab. Appl., 16:4 (1971), 620

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Teoriya Veroyatnostei i ee Primeneniya, 1971, Volume 16, Issue 4, Pages 638–648 (Mi tvp2323)

This article is cited in 6 scientific papers (total in 6 papers)

Asymptotic behaviour of the non-extinction probability for a critical Branching process

V. P. Čistyakov

Moscow

Full-text PDF (504 kB) Citations (6)

Abstract: Critical age-dependent branching processes with

$n$ types

$T_1,\dots,T_n$ of particles are considered. Let

$\mu_j^i(t)$ be the number of particles of type

$T_j$ at time

$t$ given that at time

$t=0$ there was only one particle of type

$T_i$ . We derive an asymptotic formula for the probability

$\mathbf P\{\mu_1^i(t)+\dots+ \mu_n^i(t)>0\}$ as

$t\to\infty$ .

Received: 27.02.1970

English version:
Theory of Probability and its Applications, 1971, Volume 16, Issue 4, Pages 620–630
DOI: https://doi.org/10.1137/1116069

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. P. Čistyakov, “Asymptotic behaviour of the non-extinction probability for a critical Branching process”, Teor. Veroyatnost. i Primenen., 16:4 (1971), 638–648; Theory Probab. Appl., 16:4 (1971), 620–630

Citation in format AMSBIB

\Bibitem{Chi71}

\by V.~P.~{\v C}istyakov

\paper Asymptotic behaviour of the non-extinction probability for a~critical Branching process

\jour Teor. Veroyatnost. i Primenen.

\yr 1971

\vol 16

\issue 4

\pages 638--648

\mathnet{http://mi.mathnet.ru/tvp2323}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=298782}

\zmath{https://zbmath.org/?q=an:0252.60032}

\transl

\jour Theory Probab. Appl.

\yr 1971

\vol 16

\issue 4

\pages 620--630

\crossref{https://doi.org/10.1137/1116069}

Linking options:

https://www.mathnet.ru/eng/tvp2323

https://www.mathnet.ru/eng/tvp/v16/i4/p638

This publication is cited in the following 6 articles:

V. Vatutin, A. Iksanov, V. Topchii, “A two-type Bellman–Harris process initiated by a large number of particles”, Acta Appl. Math., 138:1 (2015), 279–312
V. A. Vatutin, “On a class of the critical multitype Bellman–Harris branching processes”, Theory Probab. Appl., 25:4 (1981), 760–771
V. A. Vatutin, “Discrete limit distributions of the number of particles in a multitype age-dependent branching processes”, Theory Probab. Appl., 24:3 (1980), 509–520
V. A. Vatutin, “Asymptotic behavior of the survival probability for a decomposable branching process with replacements depending on the age of the particles”, Math. USSR-Sb., 31:1 (1977), 95–107
V. A. Vatutin, “Asymptotic behaviour of the non-extinction probability for a critical branching process”, Theory Probab. Appl., 22:1 (1977), 140–146
V. P. Chistyakov, “Limit Theorems for Age-Dependent Branching Processes”, Theory Probab. Appl., 17:1 (1972), 54–71

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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