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Uniqueness and Extinction of Weighted Markov Branching Processes |
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| Authors: | |
| Institution: | (1) School of Computing and Mathematical Sciences, The University of Greenwich, Maritime Greenwich Campus, Old Royal Naval College, The University of Greenwich, Greenwich, London, SE10 9LS, UK;(2) Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong;(3) School of Mathematical Science and Computing Technology, Central South University, Changsha, China |
| Abstract: | 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. AMS 2000 Subject Classification Primary 60 J27; Secondary 60 J80 |
| Keywords: | Markov branching process weighted Markov branching process regularity and uniqueness extinction explosion |
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