Methodology and Computing in Applied Probability

, Volume 7, Issue 4, pp 489–516 | Cite as

Uniqueness and Extinction of Weighted Markov Branching Processes



This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained.


Markov branching process weighted Markov branching process regularity and uniqueness extinction explosion 


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The authors wish to acknowledge and thank the anonymous referee and the Associate Editor for providing extremely helpful suggestions.


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.School of Computing and Mathematical Sciences, The University of Greenwich, Maritime Greenwich Campus, Old Royal Naval CollegeThe University of GreenwichGreenwichUK
  2. 2.Department of Statistics and Actuarial ScienceUniversity of Hong KongPokfulam RoadHong Kong
  3. 3.School of Mathematical Science and Computing TechnologyCentral South UniversityChangshaChina

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