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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 4, Pages 801–809 (Mi tvp28)  

This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

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

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.

DOI: https://doi.org/10.4213/tvp28

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English version:
Theory of Probability and its Applications, 2007, 51:4, 704–714

Bibliographic databases:

Received: 13.02.2006

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chen A. Li J. Chen Y. Zhou D., “Extinction Probability of Interacting Branching Collision Processes”, Adv. Appl. Probab., 44:1 (2012), 226–259  crossref  mathscinet  zmath  isi  elib  scopus
    2. Chen A. Li J. Chen Y. Zhou D., “Asymptotic Behaviour of Extinction Probability of Interacting Branching Collision Processes”, J. Appl. Probab., 51:1 (2014), 219–234  crossref  mathscinet  zmath  isi  scopus
    3. Chen A. Li X. Ku H., “a New Approach in Analyzing Extinction Probability of Markov Branching Process With Immigration and Migration”, Front. Math. China, 10:4 (2015), 733–751  crossref  mathscinet  zmath  isi  elib  scopus
    4. N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of a stage-dependent epidemic model based on a non-Markov random process”, J. Appl. Industr. Math., 14:3 (2020), 566–580  mathnet  crossref  crossref
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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