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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 4, Pages 801–809
DOI: https://doi.org/10.4213/tvp28 (Mi tvp28) 		 
This article is cited in 7 scientific papers (total in 7 papers)

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On the distribution of the number of final particles in a branching process with transformations and pairwise interactions

A. M. Lange

N. E. Bauman Moscow State Technical University
Full-text PDF (950 kB) Citations (7)
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DOI: https://doi.org/10.4213/tvp28
Abstract: A Markov continuous time branching process with two types of particles $T_1$ and $T_2$ is considered. Particles of the two types appear either as the offspring of a particle of type $T_1$, or as a result of interaction of two particles of type $T_1$. Under certain restrictions on the distribution of the number of new particles the asymptotic behavior of the expectation and variance of the number of particles of the two types are investigated and the asymptotic normality of the distribution of the number of final particles of type $T_2$ is established when the initial number of particles of type $T_1$ is large.
Keywords: branching process with interaction, final probabilities, exponential generating function, stationary first Kolmogorov equation, explicit solutions.
Received: 13.02.2006
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 4, Pages 704–714
DOI: https://doi.org/10.1137/S0040585X97982748
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. M. Lange, “On the distribution of the number of final particles in a branching process with transformations and pairwise interactions”, Teor. Veroyatnost. i Primenen., 51:4 (2006), 801–809; Theory Probab. Appl., 51:4 (2007), 704–714
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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