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Algebra i Analiz, 2024, Volume 36, Issue 4, Pages 38–56 (Mi aa1928)  

This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

On the asymptotic behavior of the average value of functionals of a random field of particles defined by a branching random walk

A. V. Lyulintsev

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
References:
Abstract: Consider a homogeneous Markov process with continuous time on the phase space $\mathbb Z_+ = \{0, 1, 2, \dots\}$, which we interpret as the movement of a particle. The particle can only transition to neighboring points in $\mathbb Z_+$, meaning that with each change in position, its coordinate changes by one unit. The process is equipped with a branching mechanism. Branching sources can be located at each point in $\mathbb Z_+$. At the moment of branching, new particles appear at the branching point and then evolve independently of each other (and of the other particles) according to the same laws as the initial particle. At each time $t$, we have a random field on $\mathbb Z_+$ consisting of particles present in the system at that moment. Functionals of this field $\sum_{(m_j, m_k)}\Phi (m_j, m_k)$ are considered, where the sum is taken over all ordered pairs $(m_j, m_k)$ of different particles in the field. The asymptotic behavior of the average value of this functional as $t \to +\infty$ is studied.
Keywords: Markov branching process, branching random walks, Jacobi matrices, orthogonal polynomials.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-289
Received: 28.10.2023
Document Type: Article
Language: Russian
Citation: A. V. Lyulintsev, “On the asymptotic behavior of the average value of functionals of a random field of particles defined by a branching random walk”, Algebra i Analiz, 36:4 (2024), 38–56
Citation in format AMSBIB
\Bibitem{Lyu24}
\by A.~V.~Lyulintsev
\paper On the asymptotic behavior of the average value of functionals of a random field of particles defined by a branching random walk
\jour Algebra i Analiz
\yr 2024
\vol 36
\issue 4
\pages 38--56
\mathnet{http://mi.mathnet.ru/aa1928}
Linking options:
  • https://www.mathnet.ru/eng/aa1928
  • https://www.mathnet.ru/eng/aa/v36/i4/p38
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:101
    Full-text PDF :3
    References:28
    First page:15
     
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