Uniqueness and Extinction of Weighted Markov Branching Processes
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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.
KeywordsMarkov 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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