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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

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Volume 28, Issue 5

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Reduced critical Bellman–Harris branching processes for small populations

Vladimir A. Vatutin / Wenming Hong
  • School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University Beijing, China
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/ Yao Ji
  • School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University Beijing, China
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Published Online: 2018-10-26 | DOI: https://doi.org/10.1515/dma-2018-0028

Abstract

A critical Bellman-Harris branching process {Z(t),t ≥ 0} with finite variance of the offspring number is considered. Assuming that 0 < Z(t) ≤ φ(t), where either φ(t) = o(t) as t → ∞ or φ(t) = at,a>0, we study the structure of the process where Z(s,t) is the number of particles in the initial process at moment s which either survive up to moment t or have a positive number of descendants at this moment.

Keywords: Bellman-Harris branching process; reduced process; conditional limit theorem

Originally published in Diskretnaya Matematika (2018) 30,No 3, 25–39 (in Russian).

Funding

The work of V.A. Vatutin was supported by the Russian Science Foundation under grant no. 14-50-00005, the work of Wenming Hong and Yao Ji was supported by Natural Science Foundation of China under grants 11531001 and 11626245.

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About the article

Received: 2018-05-17

Published Online: 2018-10-26

Published in Print: 2018-10-25


Citation Information: Discrete Mathematics and Applications, Volume 28, Issue 5, Pages 319–330, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2018-0028.

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