Science China Mathematics

, Volume 61, Issue 3, pp 545–562 | Cite as

Generalized Markov interacting branching processes

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Abstract

We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness. Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed. The mean explosion time and the total mean life time of the processes are also investigated and resolved.

Keywords

generalized Markov interacting branching process regularity extinction probability mean extinction time mean explosive time total mean life time 

MSC(2010)

60J27 60J35 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11371374 and 11571372) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110162110060).

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaChina
  2. 2.Department of MathematicsSouthern University of Science and TechnologyShenzhenChina
  3. 3.Department of Mathematical SciencesThe University of LiverpoolLiverpoolUK

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