A conditional limit theorem for a critical Branching process with immigration

  • V. A. Vatutin


The life period of a branching process with immigration begins at the moment T and has length τ if the number of particles μ(T −0)=0, μ(t)>0 for all T⩽t<T+τ, and μ(T+τ)=0 (the trajectories of the process are assumed to be continuous from the right). For a critical Markov branching process is obtained a limit theorem on the behavior of μ(t) under the condition that τ>t and T=0.


Limit Theorem Life Period Conditional Limit Conditional Limit Theorem 
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Literature cited

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    A. M. Zubkov, “Life periods of a branching process with immigration,” Teor. Veroyatn. Ee Prim.,17, No. 1, 179–188 (1972).Google Scholar
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    I. G. Petrovskii, Lectures on the Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1971).Google Scholar
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    E. Seneta, “An explicit limit theorem for the critical Galton-Watson process with immigration,” J. Roy. Statist. Soc., Ser. B,32, No. 1, 149–152 (1970).Google Scholar
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    R. Bojanic and E. Seneta, “Slowly varying functions and asymptotic relations,” J. Math. Anal. Appl.,34, No. 3, 302–315 (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • V. A. Vatutin
    • 1
  1. 1.V. A. Steklov Mathematics InstituteAcademy of Sciences of the USSRUSSR

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