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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 2, Pages 376–380
DOI: https://doi.org/10.4213/tvp3926 (Mi tvp3926) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Short Communications

On the Extinction Probability of a Branching Process with Two Kinds of Interaction of Particles

A. V. Kalinkin

N. E. Bauman Moscow State Technical University
Full-text PDF (578 kB) Citations (15)
DOI: https://doi.org/10.4213/tvp3926
Abstract: A continuous-time Markov branching process with a single type $T$ of particles is considered in which any pair of particles $T+T$ produces offspring independently of all other particles. In addition, any particle of type $T$ also produces children. Representations for the extinction probabilities of this process are obtained under certain assumptions on the offspring distribution. To establish this result we apply the exponential generating function method for the solution of a stationary backward Kolmogorov system of differential equations (see [A. V. Kalinkin, Theory Probab. Appl., 27 (1982), pp. 201–205]).
Keywords: branching process with interaction of particles, extinction probabilities, Laplace equation for the exponential generating function, explicit solutions.
Received: 24.09.1998
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 2, Pages 347–352
DOI: https://doi.org/10.1137/S0040585X97978981
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Kalinkin, “On the Extinction Probability of a Branching Process with Two Kinds of Interaction of Particles”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 376–380; Theory Probab. Appl., 46:2 (2002), 347–352
Citation in format AMSBIB
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\paper On the Extinction Probability of a Branching Process with Two Kinds of Interaction of Particles
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\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 2
\pages 347--352
\crossref{https://doi.org/10.1137/S0040585X97978981}
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  • https://www.mathnet.ru/eng/tvp/v46/i2/p376
    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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